Projects

1. VIRTUAL ENVIRONMENTS FOR THE ANALYSIS OF WELL BEING AT WORKPLACES (ALBO PROJECT)

Research objectives and questions

The ALBO project seeks to further our knowledge of well being at workplaces and the way it is surveyed and monitored. The empirical part of the research will be carried out in Italy in a number of existing organisations (a small sized municipality, two large sized companies from the pulp & paper and the building sector plus a group of SMEs from agriculture and manufacturing) that have accepted to become project pilot units.

Specifically, the research aims to explore the emergence and the dynamics of psychosocial risks among the employees of these organisations, as well as to develop innovative tools for the assessment and management of those risks according to the provisions of country specific laws and regulations.

The project focuses on the actions and behaviours of individuals working in the organisations, at any level of the hierarchy, and on the particular mechanisms through which they interact one another and within the contextual and structural aspects of their workplaces (e.g. including the means of production used, the particular conformation of the personal working space, the rules and routines adopted, the command and control chain etc.).

We suggest that the reproduction of those interaction mechanisms by means of “immersive workplaces”, or VR-like scenarios reflecting the actual experience of the individuals in their own working spaces, can offer deeper insights and better knowledge of the main risk factors than the current practice of distributing anonymous survey questionnaires in a company or conducting face-to-face interviews with selected workers.
The following specific questions will be addressed:

• How are psychosocial risks perceived by the people in a given workplace?
• To what extent do contextual and structural aspects influence this perception?
• Is this perception changing over time, and due to what?
• How can organisations properly configure an assessment & management system of the internal psychosocial risks?
• What are the drivers and the barriers to improvement?
• Is it possible to set measureable targets for improvement?

Research method

The ALBO project adopts a multiple case-study approach. This methodology enables the researchers to maintain the complexities and contextual contingencies in which the firms and the phenomena under study are embedded.
For each case study, the following data collection procedure will be set up in accordance with the top management of the selected organisation:

• Identification of a suitable number and quality of production processes and working spaces where these processes develop
• Identification of a suitable number and quality of interactive scenarios (human2human & human2machine) within each proposed working space
• Initial distribution of a “standard” questionnaire (accompanied or not by face-to-face interviews) for the collection of information on psychosocial risks and the perception thereof
• Video recording of real-life instantiations of the selected interactive scenarios, with the aim to identify the most common “misinterpretations” and “misbehaviours”
• Analysis and evaluation of the evidence collected, in terms of a list of key factors of risk for each proposed working space
• Discussion of the results with the top management and definition of preventive and/or corrective actions
• Distribution of a “revised” questionnaire (and/or face-to-face interviews) taking stock of the previous activities and results

Acting in parallel on all project pilots, this phase is expected to last about six months. It is at this stage than the material collected as described above should be turned into short “VR-like scenarios” tailored on the real-life processes, workspaces, interaction mechanisms, and psychosocial risks examined in the previous phase, and where the real-life actors will be modelled by the use of avatars.
These scenarios will be returned to the people involved and technically refined in close collaboration with them. It is foreseen to create simulated sessions of usage, either with different people belonging to the same organisation, or with different organisations active in the same business sectors.
In association with each of these scenarios, a set of performance indicators will be defined and a number of evaluative questions, points of decision, proposed action items will be introduced in alternance with the storyboard developments. Individual performance will be measured by the set of indicators and in accordance with the “score” achieved at the end of the “game”. This score will be made totally transparent to both the employee and the top management of the organisation (s)he belongs to.

ject intends to analyze theoretically and experimentally the processes of learning and information diffusion in presence of heterogeneous agents. Within economics,

2. LEARNING AND INFORMATION DIFFUSION WITH HETEROGENEOUS AGENTS UNDER UNCERTAINTY. THEORETICAL AND EXPERIMENTAL ANALYSIS

Abstract. The research project intends to analyze theoretically and experimentally the processes of learning and information diffusion in presence of heterogeneous agents. Within economics, the analysis of how knowledge is shared within networks or among strategic players has recently developed independently in various directions. A very common assumption in this literature is that individuals are fully rational and homogenous agents that receive information or establish links of equivalent value. Empirically, these postulates are questionable. Individuals usually exhibit different, sometimes even contradictory, heuristic procedures and the sharing of knowledge is often triggered by local interaction that produces non-linear transformations in aggregate behaviour. Theoretically, the network formation literature has introduced heterogeneity by considering different types of agents defined by the cost of link formation. However, the processes of learning in networks of agents are difficult to investigate in the field, because of potentially confounding factors. In contrast, laboratory experimentation allows for careful control of the effect of these factors. We specifically intend to test experimentally how learning is affected by various kinds of heterogeneity. This will be done by analyzing the processes of two-sided network formation with social distance among the subjects, the effect of the introduction of different types of players in strategic environments and the robustness of informational cascades with subjects differentiated both in terms of private information and heuristic procedures when facing costly sequential but endogenous information. We expect that laboratory data will be useful to propose a comprehensive analysis of the dynamics of learning incorporating the hypotheses that agents are not purely self-regarding maximizers, have bounded rationality and exhibit information-processing biases.

State of the art. The processes of information diffusion in a population have attracted increasing interest among economists. A key issue in this field of research is how these processes affect shared knowledge and, more generally, enhances social learning. Within economics, the analysis of this problem has developed independently in various directions by recasting different strands of literature.

A first approach is characterized by the introduction of publicly released information in models in which consensus can be reached by non-strategic agents, that is, they do not try to gain additional information by interacting with other agents (Nielsen et al. 1990).

In the literature on social networks, on the other hand, individuals are identified with the vertices of a graph and have pair wise relationships within their relational neighborhoods. The level of connectedness of the network measures the “conformism” within the population and determines the benefits accruing to individuals from the participation to the network (Goyal 2005).

Finally, strategic experimentation models assume that players can gain beneficial information by explicitly interacting, observing or exchanging advices with each other. Within this approach herding behaviour can be the result of informational cascades or also information manipulation (Bikhchandani et al. 1992).

A common assumption in this literature is homogeneity, according to which all decision makers exhibit the same kind of rationality and conjecture that others receive information or establish links of equivalent value.

Empirically, both these postulates are questionable. Individuals usually determine strategically how to take into account signals or advices released by others and they suppose that someone is better informed than others are. Sharing of knowledge is often triggered by the incremental decisions taken by locally interacting individuals that produce non-linear transformations in aggregate behaviour primarily by virtue of the multiple differentiation of the subjects.

Theoretically, the assumption of homogenous agents is constraining since “the sum of the behaviour of simple economically plausible individuals may generate complicate dynamics, whereas constructing one individual whose behavior has these dynamics may lead to that individual having very unnatural characteristics” (Kirman 1992, 118).

In the network formation literature the effect of agents heterogeneity has been mostly introduced by considering agent type defined by the cost of link formation or by the value to other agents of forming a link with that type. The static model by Johnson and Gilles (2000) introduced a spatial cost topology, representing geographical, social or individual differences, in the ‘two-sided’ network formation model of Jackson and Wolinsky (1996). This model, in which two agents must agree on the decision to form a mutual link, but defection by one agent is sufficient to break the link, is well suited to represent economic situations such R&D collaborations between firms (Caminati 2006). Dynamic models of network formation (Watts 2001) open the possibility that agents heterogeneity acts through a conditioning of the meeting process, rather than the influence on cost and/or value of link formation. Carayol and Roux (2003) introduce a non uniform meeting probability in a ‘two sided’ dynamic model in which agents make small random errors in their link decisions as in Jackson and Watts (2002) and obtain that the selected equilibria do not fall systematically under the usual categories.

The consideration of heterogeneous agents also imposes a critical re-appraisal of the “self-regarding” human behaviour portrayed by rational choice theory. More recently, behavioural economics on the theoretical side, and experimental economics on the applied side, have contended orthodox rational choice theory. The legitimacy of considering the “self-regarding” agent as the “representative” agent in economic modelling has been put under scrutiny and strongly questioned (Innocenti and Pazienza 2006). Building upon systematic deviations from the selfish behaviour showed by theoretical paradoxes and experimental evidence, many economists are presently working on the hypothesis that heterogeneity across the agents’ motives allows a cooperative solution to be reached in on games with conflict of interest. In particular, the type named “conditional cooperator” has been introduced, that is an agent who is willing to cooperate provided that the other individuals involved in social interactions are equally committed (Fehr and Fischbacher 2002). The presence in a population of individuals motivated by a reciprocation attitude, a sufficiently large number of which can be found interacting on a regular basis with the multitude of “straightforward maximizers”, has been shown to be crucial in making public goods provision possible (Fischbacher, Gachter, and Fehr 2001).

Finally, agents heterogeneity can be a useful assumption to explain herding behaviour that has been modelled rationally under the heading of informational cascades. After the seminal theoretical contribution of Bikhchandani et al. (1992), a wide experimental literature has tested the empirical robustness of this kind of behaviour, according to which, in particular conditions of sequential choice, earlier decision makers’ choices of an action can provide sufficient evidence to make it rational for later decision makers to ignore their own private information and to mimic previous choices. Anderson and Holt (1997) were the first to provide evidence of the occurrence of informational cascades in the laboratory, which was confirmed by more recent papers, including Allsop and Hey (2000) and Hung and Plott (2001). In these contributions the quality and the quantity of the released signals are the same for all subjects. This assumption prevents from analysing the processes of information dissemination from better (insiders) to less informed (outsiders) subjects, which has been object of theoretical analysis (Thaler and Ziemba 1988) and of empirical investigation (Schnytzer-Shilony 1995). In these works inside information is captured by means of proxies implying an imperfect definition of optimal choices. In contrast, laboratory environment makes it possible to control information flows and to check the effect of the asymmetrical endowment of costly private sequential information and to detect if subjects are differentiated in terms of the heuristic procedures exhibited in the activity of information-gathering and processing.

Most experimental work on network formation (Kosfeld 2004) has considered the ‘one sided’ non-cooperative framework of Bala and Goyal (2000). We intend to extend experimental analysis to analyze different levels of interaction complexity, going from the ‘two sided’ model of network formation to the two-player non-cooperative games, and to the sequential representation of learning as informational cascades.

A first part of the project will implement an experimental study of a dynamic ‘two sided’ model of network formation which is well suited to capture relevant examples of social learning such as R&D collaboration networks. We aim at considering the effects of agents’ heterogeneity introduced through a fixed exogenous metric of geographic, technological or social distance which adds to the effects of the endogenously evolving relational distance. Unlike the laboratory study of Deck and Johnson (2002), in which geographical distance affects the cost of link formation, we intend to address the case explored by Carayol and Roux (2003; 2004) in which the exogenous metric affects the probability that two agents ‘meet’ and have thus an opportunity to form or break a link. The opportunity of social interaction offered by a sufficiently close ‘geographical’ distance is particularly relevant in situations where agents are imperfectly informed about the network structure, so that the knowledge externalities accessed through a link with one agent are not known before interacting with the agent in question. In a more complex design, we intend to address the case in which agent type is defined by one or more characteristics, beside location, and information about the latter does not fully reveal information about the former. For instance, the profitable sharing of knowledge between technologically distant firms, although less likely, may nevertheless produce radical innovations. Our laboratory experiment will also test the prediction of Carayol and Roux (2003) that different values of the knowledge transferability parameter generate qualitatively different network architectures.

The mechanics of social learning has also been modelled in terms of sequential learning by means of the notion of informational cascades. Two basic assumptions of theoretical and experimental literature on informational cascade and herding behaviour are that decisions are made sequentially according to a predetermined order and that each decision maker assumes that other individuals receive signals of identical accuracy. In contrast, actual individuals usually determine strategically the timing of decision, even without observability (Caminati, Innocenti and Ricciuti 2006), and their common conjecture is that someone is better informed than others are. For example, in horse race betting markets bettors are generally perceived as divided in insider and outsider, decide autonomously when place a betting and the costs of waiting before the deadline are very low. The same feature characterizes competitive financial markets that are sufficiently thick. But the main reason for waiting in real environments like those mentioned above is just to find out what are the best informed subjects. This feature exposes imperfectly informed subjects to the risk of information manipulation. To analyze in the laboratory this specific situation we intend to make two sets of experiments. In the first “baseline” set we will introduce two types of subjects, insider and outsiders, differentiated by the degree of the accuracy of their information. Our experimental design will follow that of Anderson-Holt (1997) with the introduction of endogenous timing as in Sgroi (2003). We will test different versions of the design in order to detect the effect of various degrees of signal accuracy and of different waiting costs. In the second “heterogeneous” set of experiments we will introduce explicit form of subjects heterogeneity by organizing sessions divided in two phases. In the first period, we will discriminate among subjects by submitting them to a choice procedure to detect if they make their predictions by adhering to or by systematically deviating from Bayes’ rule. Previous experimental work (Anderson and Holt 1997, and Nöth and Weber 2003) shows that the most frequent biases are that some subjects put more weight on their private information and do not use publicly released information adequately, i.e. overconfident agents tend to perceive themselves to be more competent (Fox and Tversky 1995), while others predict the urn that receives the greatest number of observed and inferred signals and ignore those following the formation of a cascade (counting heuristic). In the second period, we will perform sessions of the “baseline” design in order to investigate the effect of different compositions of the set of subjects. In this way we intend to analyse how specific cognitive biases determine the development or the collapse of informational cascades in presence of heterogeneous agents.

The introduction of limitedly rational subjects also raises the issue of the validity of the assumption of the self-regarding representative agent. In this context, we intend to show that the search for a model of individual behaviour posited in between selfish maximizers and altruists, that is, the “conditional cooperator,” should not be confined to the theoretical construction of a different type, but can also be usefully conceived as part of the research line studying the roots of the social capital (Putnam 1993). Therefore, we plan to carry out an experimental exercise in which what might be called a “selfish cooperation” (SC) does not denote a different type, but the behaviour the players adopt once they are embedded in a peculiar strategic environment. A SC can be defined as the individual who, while being a self-regarding type, cooperates in a “game environment” apt to allow the Bayesian updating to sustain the probability of cooperation by the other player. We claim that this kind of game environment is provided by the Centipede Game (Rosenthal 1981).

As well-known, in the Centipede backward induction dictates the player 1 to play “down” at the first stage of the game. Yet, it can be shown that in this game selfish individuals cooperate not just whenever the first player makes an erroneous move, or due to the enforcement of a social norm by punishment, but because of social learning promoting cooperative behaviour. The peculiar feature of this game in extensive form – to assign to each player, in alternation node-by-node, a lower and an increased payoff – can be exploited by the players’ cooperative behaviour aimed at letting the crop grow till the final node. The experimental design will be centred in the so-called “Strategy Method”, whereby Player 2 of the Centipede may decide to go on, or not – after player 1 has violated backward induction by playing “forward” at the first stage of the game – being informed about his complete strategy in a pre-game, the Trust Game. Player 1 may go on as well, or not, depending on the information which is communicated to him, about the full set of replies, that is the amount sent back for each proposed split of the money in the preliminary Trust Game by his opponent.

Proposed methodologies: All the models of social learning with heterogeneous agents will be tested experimentally. The laboratory of experimental economics LabSi (http://www.labsi.org) of the University of Siena will provide the technical and the practical support for the experiments.

Experimental techniques will follow the standard methodology. Experimental tests need to be derived from repeated set-up with many trials and agents. Some experiments will be computerized using the software Z-tree provided by the University of Zurich. During the sessions the subjects will be seated at computer terminals in separate seats to prevent communication or visual contact among them. For each experiment we will conduct pilot experiments. If permitted by experimental purpose and design, we will adopt double blind procedures in order to guarantee absolute anonymity of choices. The dataset will be first analyzed qualitatively and then quantitatively by means of statistical packages like STATA and SPSS.

Expected achievements: We expect that evidence collected in the laboratory data will be useful to propose a comprehensive analysis of social learning incorporating the hypotheses that that agents are not purely self-regarding maximizers, have bounded rationality and exhibit information-processing biases.

With respect to the “two sided” dynamic model of network formation, we expect that introducing an exogenous metric of ‘geographical’ or social distance, which is uncorrelated or imperfectly correlated with other characteristics of ‘type’, will provide new insights on the influence of social capital on economic decisions and on the effects of knowledge externalities. If living in close ‘geographical’ neighbourhoods offers higher opportunities of social interaction, the effects on network architecture may depend, in the first place, on the strength of knowledge externalities – as predicted by Carayol and Roux (2003) model – and in the second place on the nature of the correlation between ‘geographical’ distance and the pay-off relevant characters of the agent type (as we expect). For instance, geographical distance may be positively correlated with the cost of link formation, but may be also positively correlated with the value of the information exchange enabled by a far reaching link. Our laboratory data will also provide new evidence for a dynamic model of network formation incorporating the hypothesis that boundedly rational agents make errors in their decisions of link formation.

As for the mechanics of network formation, the introduction of subjects’ heterogeneity should provide useful insights into the actual dynamics of herd behaviour and enhance the analytical capability to predict the possibility of information manipulation. We expect that the robustness of informational cascade will be generally confirmed in the laboratory. In the “baseline” experiments subjects with more accurate signals will have an incentive to decide earlier. If waiting costs are high, the other subjects will mimic immediately the first mover no matter what their private signals are because they infer that their precision levels are dominated by the first mover. This implies that later decisions will not convey any additional information. This behaviour should create an almost instantaneous informational cascade. In presence of specific biases such as overconfidence this effect can lead to situations in which better informed subjects decide too fast and thus generate misleading signals for others. In different versions of the experimental design with lower costs and different degrees of signal accuracy the dynamics of choices should become more complex and also provide useful evidence to analyse how participants can distinguish between informative and uninformative decisions and protect themselves from the risk of information manipulation. The second set of experiments should provide further insight by showing the effect of specific information-processing biases on the robustness of informational cascades.

In the experiments on “selfish cooperation” we should categorise our subjects in three types, that are selfish, selfish cooperators, and straight cooperators according to the choices spelled out in the pre-trust game. We also expect to find significant differences in the behaviour of subjects according to their matching in the Centipede. For example, selfish cooperators will tend to exit earlier when coupled with straight selfish individuals, and to move forward when matched with cooperators. Finally, we anticipate finding significant differences by comparing treatments in which subjects know the type of their opponents and control-treatments in which this information is not given to subjects.

References

• Allsopp, L. and J. D. Hey (2000) “Two Experiments to Test a Model of Herd Behavior” Experimental Economics, 2000, 3:121-36
• Anderson, R. and C. Holt (1997) “Information Cascades in the Laboratory” American Economic Review, 87:847-64.
• Bala, V. and S. Goyal (2000) “A Noncooperative Model of Network Formation” Econometrica, 68:1181-230
• Bikhchandani, S., D. Hirshleifer, and I. Welch (1992) “A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades” Journal of Political Economy, 100: 992-1026.
• Caminati, M. (2006) “Knowledge Growth, Complexity and the Returns to R&D” Journal of Evolutionary Economics, 16:207-29
• Caminati, M., A. Innocenti, and R. Ricciuti (2006) “Drift Effect and Timing without Observability” Journal of Economic Behavior & Organization, 61:393-414
• Carayol, N. and P. Roux (2003) “Network formation in a model of distributed innovation” mimeo, ETA, Universite Louis Pasteur
• Carayol, N., and P. Roux (2004) “Behavioral foundations and equilibrium notions for social network formation processes” Advances in Complex Systems, 7:77-92
• Camerer, C., D. Lovallo (1999) “Overconfidence and Excess Entry: An Experimental Approach” The American Economic Review, 89:306-18
• Deck, C. and C. Johnson (2002) “Link Bidding in a Laboratory Experiment” mimeo, University of Arkansas.
• Fehr, E. and U. Fischbacher (2002) “Why Social Preferences Matter – The Impact of Nonselfish Motives on Competition, Cooperation, and Incentives” Economic Journal, 112:C1-C33
• Fischbacher, U., S. Gächter, and E. Fehr (2001) “Are People Conditionally Cooperative? Evidence from a Public Goods Experiment” Economics Letters, 71:397-404
• Fox, C. R., and Tversky, A. (1995) “Ambiguity Aversion and Comparative Ignorance” Quarterly Journal of Economics 110:585-603
• Goyal,S.(2005) “Learning in networks: a survey paper” in G. Demange and M. Wooders, eds, Group formation in economics: Networks, clubs and coalitions, Cambridge University Press
• Hung, A. and C. Plott (2001) “Information Cascades: Replication and an Extension to Majority Rule and Conformity-Rewarding Institutions” American Economic Review, 91:1508-20
• Innocenti A. and M. G. Pazienza (2006) “Altruism and Gender in the Trust Game” Labsi Working Paper, University of Siena, n. 5 (forthcoming in A. Innocenti and P. Sbriglia eds, “Games, Rationality and Behaviour. Essays on Behavioural Game Theory and Experiments”, Palgrave-Macmillan)
• Jackson, M.O. and A. Watts (2002) “The Evolution of Social and Economic Networks” Journal of Economic Theory, 71:44-74
• Jackson, M. and A. Wolinsky (1996) “A strategic model of social and economic networks” Journal of Economic Theory, 71:440-74
• Johnson, C. and R. P. Gilles (2000) “Spatial Social Network” Review of Economic Design, 5:273-300
• Kosfeld, M. (2004) “Economic Networks in the Laboratory: A Survey” Review of Network Economics, 3:20-41
• Kirman, A. P. (1992) “Whom or what does the representative individual represent?” Journal of Economic Perspectives, 6:117-136
• Nielsen, L. T., A. Brandenburger, J. Geanakoplos, and R. McKelvey, T. Page (1990) “Common Knowledge of an Aggregate of Expectations” Econometrica, 58:1235-39
• Noth, M. and M. Weber (2003) “Information Aggregation with Random Ordering: Cascades and Overconfidence” The Economic Journal, 113:166–89
• Putnam, R. (1993) Making Democracy Work: Civic Traditions in Modern Italy, Princeton, NJ, Princeton University Press.
• Rosenthal, R. W. (1981) “Games of perfect information, predatory pricing and the chain-store paradox” Journal of Economic Theory, 25:92-100
• Schnytzer, A. and Y. Shilony (1995) “Inside Information in a Betting Market” The Economic Journal, 105:963-71
• Sgroi, D. (2003) “The Right Choice at the Right Time: A Herding Experiment in Endogenous Time” Experimental Economics, 6:159–80
• Thaler, R. H. and W. T. Ziemba (1988) “Anomalies: Parimutuel Betting Markets: Racetracks and Lotteries” The Journal of Economic Perspectives, 2:161-174
• Watts, A. (2001) “A Dynamic Model of Network Formation” Games and Economic Behavior, 34:331-41.

2. SOCIAL LEARNING, INFORMATIONAL CASCADES AND ASSET MARKETS UNDER RISK AND AMBIGUITY

Abstract.  The theme of the research project can be classified under two main headings: social learning and informational cascades and asset pricing.
The first part of the project intends to analyze the processes of social learning and information diffusion. Specifically, we plan to test experimentally and to investigate empirically how social learning is affected by various kinds of agent heterogeneity. This will be done by analyzing the effect of the introduction of different types of players in strategic environments and by testing the robustness of informational cascades with subjects differentiated both in terms of private information and of heuristic procedures. We will set up experimental designs concerning various strategic games, in order to analyze which kind of social learning, under which motivating environment, is more effective in the process of information collecting and in orienting agents to set up utility functions that take into account the other individuals’ payoffs. We expect that laboratory data will be useful to suggest a comprehensive analysis of the dynamics of learning incorporating the hypotheses that agents’ behaviour is not purely self-regarding, departs from perfect rationality and exhibits individually differentiated cognitive biases. From our experimental settings we also expect to detect to what extent different quantity and quality of information inserted in the experimental design will foster the social learning which is needed to have the agents to select the particular equilibrium path corresponding to the emergence of cooperation. This should allow us to show whether structural or strategic uncertainty counts more, namely whether the environmental context or the players’ information about the other agents’ types is more influential on individual disposition to reciprocate in simultaneous and sequential games. The second part of the project aims at investigating both theoretically and experimentally the asset pricing implications of the probability weighting function. According to Tversky and Kahneman’s (1992) Cumulative Prospect Theory, agents evaluate assets using a value that is concave over gains and convex over losses. Further, instead of representing beliefs through a standard probability function, agents are supposed to use probabilities distorted by applying a weighting function. The main consequence of this assumption is to overweight the tails of the distribution and this overweighting does not represent a bias in beliefs; it is simply a modelling device for capturing the common preference for a lottery-like, or positively skewed, wealth distribution. We intend to apply this behavioural assumption in an economy with normally distributed security payoffs and homogeneous investors, and check both theoretically and experimentally if the pricing implications of Cumulative Prospect Theory are different from those of standard approaches. Crucially we will assume that agents have a different attitude between very large gains and losses. In this way we expect to have a better proxy to observed puzzling financial phenomena such as private equity, low average return on Initial Public Offers and the lack of diversification in many portfolios. Indeed we wish to improve the promising results obtained in previous works (Barberis at al 2001, Basili et al 2008) by explicitly considering the consequences of a probability weighted function.

State of the art.  The two themes investigated by this research project have been the subject of intense theoretical and experimental scrutiny over the past twenty years. This dialogue between modelling and laboratory activity has achieved sensible progresses mainly through the use of behavioural and non-standard theories of decision under ambiguity.
Since the early 1990s the debate on social learning has focused on the processes of information diffusion in a population. Strategic experimentation models assume that players can gain beneficial information by explicitly interacting, observing or exchanging advices with each other. Within this approach, herding behaviour can be the result of informational cascades (Bikhchandani et al 1992). A common assumption in this literature is homogeneity, according to which all decision makers exhibit the same kind of rationality and conjecture that others receive information or establish links of equivalent value. Empirically, both these postulates are questionable. Individuals usually determine strategically how to take into account signals or advices released by others and suppose that someone is better informed than others are. Theoretically, the assumption of homogenous agents is constraining since “the sum of the behaviour of simple economically plausible individuals may generate complicate dynamics, whereas constructing one individual whose behaviour has these dynamics may lead to that individual having very unnatural characteristics” (Kirman 1992, p 118). Anderson and Holt (1997) were the first to provide evidence of the occurrence of informational cascades in the laboratory, which was confirmed by more recent papers, including Allsop and Hey (2000) and Hung and Plott (2001). In these contributions the quality and the quantity of the released signals are the same for all subjects. However, this assumption excludes from the analysis the processes of information dissemination from better (insiders) to less informed (outsiders) subjects. In these works inside information is captured by means of proxies implying an imperfect definition of optimal choices.
The removal of the hypotheses of agents’ perfect rationality and homogeneity also introduces the distinction between structural uncertainty and strategic uncertainty. Differently from the uncertainty related to the objective states of the world, strategic uncertainty deals with how individuals behave and requires to model expectations regarding the other agents’ types. In dynamic models, the equilibrium selection process is affected by how agents learn and modify their behaviour when processing information about the other agents as well as the game-form. The experimental literature concerning social learning has significantly fostered the investigation of strategic uncertainty. A recent stream of literature extends the study of social learning to the area of social preferences. The basic hypothesis underlying these works is that people do care about others’ payoffs. To motivate this deviation from Expected Utility Theory, the “type” named “conditional cooperator” has been introduced, that is the agent who is willing to cooperate provided that the other individuals involved in social interactions are equally committed (Fehr and Fischbacher, 2002; Fischbacher et al 2001). In fact, theoretical models and experimental evidence show that other-regarding distributional preferences can stem from information on the co-players ethical and cooperative type (Bolton et al 1998).
The second theme of our project concerns the activity of pricing in assets markets. Over the past two decades, a great amount of work has supported the theory that, when people evaluate risks, they often depart from the predictions of expected utility and adhere to rules that can be defined non-expected utility models. In particular, a stream has been developed following Kahneman and Tversky’s modelling of human behaviour through Prospect Theory (Kahneman and Tversky 1979) and Cumulative Prospect Theory (Tversky and Kahneman 1992). In the latter theory, agents evaluate assets using a value function defined over gains and losses, which is concave over gains and convex over losses and is kinked at a given point named reference point. Crucially, instead of using probabilities directly, agents transform probabilities into distorted probabilities by applying a weighting function. There is a large literature on the pricing implications of Prospect Theory focusing mainly on the implications of the kink in the value function. In an applied paper, Basili et al (2008) show that, in a Lucas economy, in which an individual investor derives her direct utility from both consumption and fluctuations in the value of financial wealth, Prospect Theory with multiple reference points significantly improves the ability of the Barberis et al (2001) pricing model to explain facts observed in financial markets.

Description of the research projects.  This research project aims to provide theoretical and experimental answers to the following two specific questions. The first is how the processes of learning and information diffusion are influenced by various kinds of agents’ heterogeneity. The second is what are the asset pricing implications of the probability weighting function postulated by Cumulative Prospect Theory.
The first object of our project will be to analyze the mechanics of social learning by means of the notion of informational cascades. Two basic assumptions of theoretical and experimental literature on informational cascade and herding behaviour are that decisions are made sequentially according to a predetermined order and that each decision maker assumes that other individuals receive signals of identical accuracy. In contrast, actual individuals usually determine strategically the timing of decision, even without observability (Caminati et al 2006), and their common conjecture is that someone is better informed than others are. For example, in horse race betting markets bettors are generally perceived as divided in insider and outsider, decide autonomously when place a betting and the costs of waiting before the deadline are very low. The same feature characterizes competitive financial markets that are sufficiently thick. But the main reason for waiting in real environments like those mentioned above is just to find out what are the best informed subjects. This feature exposes imperfectly informed subjects to the risk of information manipulation.
To analyze in the laboratory this specific situation we intend to make two different sets of experiments. In the first “baseline” set we will introduce two types of subjects, insider and outsiders, differentiated by the degree of the accuracy of their information. We will test different versions of the design in order to detect the effect of various degrees of signal accuracy and of different waiting costs. In the second “heterogeneous” set of experiments we will introduce explicit kinds of subjects heterogeneity by studying the processes of information collecting and processing also by means of the eye-tracking procedure. We expect that evidence collected in the laboratory data will be useful to propose a comprehensive analysis of social learning incorporating the hypotheses that agents are not purely self-regarding maximizers, are not perfectly rational and exhibit cognitive biases.
An important application of the informational cascade model is betting markets. According the Bayesian model, bettors uses their subjective beliefs over the different possible states of the world and apply Bayes’ Rule to update their beliefs. Yet a large and growing body of psychological research suggests that the way people process information often departs systematically and idiosyncratically from Bayesian updating. In particular, Rabin and Shrag (1999) model and explore the consequences of one specific departure from Bayesian rationality, that is confirmatory bias. A decision maker suffers from confirmatory bias if he tends to misinterpret ambiguous evidence as confirming his current hypotheses about the world. Confirmatory bias leads to overconfidence, in the sense that people on average believe more strongly than they should in their favored hypotheses.
In this model, an agent initially believes that each of two possible states of the world is equally likely. The agent then receives a series of independent and identically distributed signals that are correlated with the true state. To model confirmatory bias, we assume that when the agent gets a signal that is counter to the hypothesis he currently believes is more likely, there is a positive probability that he misreads that signal as supporting his current hypothesis. The agent is unaware that he is misreading evidence in this way and engages in Bayesian updating that would be fully rational given his environment if he were not misreading evidence. The model also shows that an agent who suffers from confirmatory bias may come to believe in a hypothesis that is probably wrong, meaning that a Bayesian observer who was aware of the agent’s confirmatory bias would, after observing the agent’s beliefs, favor a different hypothesis than the agent. Even an infinite amount of information does not necessarily overcome the effects of confirmatory bias: over time an agent may with positive probability come to believe with near certainty in the wrong hypothesis.
We intend to test the confirmatory bias by using a unique dataset of bets on the Italian Football League in 2004/05. We will use information on individual betters (gender, age, employment), on each bet (amount, timing, odds), and on football teams (ranking, changes of the players and of the trainer). We would intend to investigate whether winning or loosing a match at the beginning or in the middle of the season has a different effect on the information set of the bettor and to provide a representation of the procedures used for this purpose that take into account bettors’ heterogeneity.
We also aim at contributing to the stream of experimental literature dealing with social learning by analyzing equilibrium selection in strategic interaction settings. We will analyze the departure from the from self-interested individual behaviour, with a particular attention to the reciprocating behaviour implied by other-regarding preferences and by subjects’ heterogeneity. To this extent, a central aspect is to study how social learning about the other agents’ types helps agents to make plans and beliefs mutually consistent (Farina and Sbriglia, 2007). Departure from the self-interested behaviour may result as an effect of reciprocal or altruistic preferences fostered by the agents’ learning about the other agents’ disposition to reciprocate, and also as an effect of the social context. In fact, we will assume that opportunities for conditional cooperation may arise depending on the mixture of different levels of pay-offs and of the specific setting of strategic interaction created by information allowing each player to set-up beliefs about the other player’s moves. We will set up experimental designs concerning various strategic games, in order to analyze which kind of social learning, under which motivating environment, is more effective in orienting agents to set up utility functions which take into account the other individuals’ payoffs. From our experimental settings we expect to be able to detect to what extent different quantity and quality of information inserted in the experimental design will foster the social learning which is needed to have the agents to select – from many possible paths of the game – the particular equilibrium path corresponding to conditional cooperation. This should allow us to show whether structural or strategic uncertainty counts more, namely whether the environmental context or the players’ information about the other agents’ types is more influential on individual disposition to reciprocate in simultaneous and sequential games
Finally, we intend to study, in the framework derived from Basili et al (2008), an economy with normally distributed security payoffs and check if the pricing implications of CPT are different from those of standard approaches. Tversky and Kahneman (1992) propose the functional form that shows a distortion of priors by a known factor. By this way, Tversky and Kahneman captures the supposed features of the weighting function: the overweighting of low probabilities and the greater sensitivity to changes in probability at higher probability levels. We will introduce this parameter in our model. As a consequence, we will study a Lucas economy with numerical techniques which estimate integer-differential equations in discrete time. Those equations are derived from stochastic optimization, that is outcomes depend on time by updating of state variables, that reflect the evolution of the whole economy. We will use a iterative process starting from initial data to find the solution. Then, we will study stability conditions and the speed of the algorithm convergence. Integrals, as expected values, are evaluated by means of the Gauss-Legendre method with the aim of obtaining a model solution that approximates the empirical observations of values related to the integer-differential equations defined. Optimization process requires calibration techniques, such as quadratic sequential algorithm to reduce difficulty of numerical estimations. To represent distorted beliefs we will introduce skewness in the revenues of assets. Then, differently from Basili et al (2008), revenues are concentrated (i.e. the mass of distribution is concentrated) on the tails, respectively on the left tail (right-skewed) or on the right tail (left-skewed). Crucially we assume that agents have a different attitude, indeed symmetric attitude, between very large gains and losses, than right-skewed and left-skewed as in Basili et al (2005). We expect to have a better proxy to observed financial phenomena (puzzles) such as private equity, low average return on Initial Public Offers and the lack of diversification in many agent portfolios.

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