Coordination Failure in Repeated Games with Almost-Public Monitoring

Some private-monitoring games, that is, games with no public histories, can have histories that are almost public. These games are the natural result of perturbing public-monitoring games towards private monitoring. We explore the extent to which it is possible to coordinate continuation play in such games. It is always possible to coordinate continuation play by requiring behavior to have bounded recall (i.e., there is a bound L such that in any period, the last L signals are sufficient to determine behavior). We show that, in games with general almost-public private monitoring, this is essentially the only behavior that can coordinate continuation play.Repeated games, Private monitoring, Almost-public monitoring, Coordination, Bounded recall

Coordination Failure in Repeated Games with Almost-Public Monitoring

Some private-monitoring games, that is, games with no public histories, can have histories that are almost public. These games are the natural result of perturbing public monitoring games towards private monitoring. We explore the extent to which it is possible to coordinate continuation play in such games. It is always possible to coordinate continuation play by requiring behavior to have bounded recall (i.e., there is a bound L such that in any period, the last L signals are sufficient to determine behavior). We show that, in games with general almost-public private monitoring, this is essentially the only behavior that can coordinate continuation play.repeated games, private monitoring, almost-public monitoring, coordination, bounded recall

Essays on learning in games and social contexts

This dissertation studies the long-run outcome of learning in the prisoner's dilemma and in auctions as well as the occurrence of herds in social contexts

Evolution in Structured Populations

How does social and economic interaction of agents within large populations depend on their perception of the matching-structure? When do evolutionary dynamics with limited information processing lead to stable outcomes prescribed by rational concepts? In the chapter "Anticipated Stability in Social and Economic Networks", I model agents to meet with non-uniform probabilities. As friends or colleagues are more likely to interact frequently, this deviation seems to be plausible. A comfortable approach to model such conditional interaction is the one of network formation. I transfer Jackson & Wolinsky (1996) and its dynamic interpretation Jackson & Watts (2002) to a non-cooperative model of network formation. Unsurprisingly, a pairwise stable network results from a Nash equilibrium. My focus rather is on closed cycles. A closed cycle is a subset of networks all of whose members are active periodically. Such a set could also be interpreted as a random graph. Jackson & Watts (2002) show that the process of network formation eventually stops in a pairwise stable network or is stuck in a closed cycle. The point of my paper is that this result crucially depends on the assumption of myopic optimization. I propose that agents may hold beliefs that are consistent with actual behavior for networks that have distance less than κ to the current network and optimize given these beliefs. The parameter κ captures the computational capabilites of the agents. If κ is large enough, small cycles can be excluded if agents anticipate such cycles. I define anticipated stability as the result of optimization given consistent beliefs around the current network. If κ is very large, agents are required to hold sophisticated beliefs for any network, as for example in Dutta, Ghosal and Ray (2005). For large populations this requirement seems inplausible to me since the number of dimensions of the strategy space grows fast with the population size. My concept can flexibly be adapted to small and large populations by fixing a large or small κ. It may seem promising to apply this concept to infinite game trees in which a distance function on the set of nodes is plausible. In the chapter "Evolution and Correlated Equilibrium" I define a game in strategic form in which players receive signals and choose strategies. According to Aumann (1987), rational play induces a correlated equilibrium distribution on the set of outcomes. Players are rational if they compute conditional probabilities of signals received by other players and optimize given this information and equilibrium strategies of their opponents. I analyze a setting in which players do not know the signal generating process, are not able to apply Bayes’ rule and do not hold beliefs over the set of strategies chosen by their opponents. I approach the concept of correlated equilibrium by an evolutionary methodology and show that even if agents display extreme bounded rationality some correlated equilibria remain to be plausible (are stable with respect to imitation dynamics). The general formulation of the signal generation encompasses Lenzo & Sarver 2005 and Mailath, Samuelson & Shaked (1997). I apply the concept of strict equilibrium sets by Balkenborg (1994) and characterize hereby asymptotically stable sets of correlated equilibrium strategies with respect to convex monotonic dynamics Hofbauer & Weuibull (1996). Balkenborg & Schlag (2007) and Cressman (2003) show similar characterizations with respect to distinct dynamics. With this framework at hand I turn to characterize robust signals. In which situations agents would not influence the signal generating process if they could? I show that if one requires asymptotically stable behavior given signals, only signals inducing strict Nash equilibria yield no incentives to influence the process of signals. If one only imposes the weaker requirement of Aumann’s rational play, I show for the example of the Chicken Game that only those signals are robust to manipulation if equilibrium play yields payoffs within the convex hull of the Nash-payoffs. It remains to be studied whether this implication transfers to other games. The third chapter "Persistent Ideologies in an Evolutionary Setting" was inspired by the discussion on religious topics partially initiated by Richard Dawkins. From my point of view, religion attaches a set of unverifiable consequences to the set of material consequences of interaction. I show that a religion that views these consequences qualitatively different from the material consequences may face no disatvantage even if agents adopt this religion more frequently if the recommend behavior yields relatively high material payoffs. I hereby critizise the approach of selecting certain preferences by evolutionary methods, as my approach allows for more general interpretations as ideologies or preferences. I generalize Sandholm (2001) in which agents are biased to one of two actions in symmetric games. In my model agents hold biases for outcomes of general asymmetric games in normal form. I assume that agents choose optimal actions given their bias and given their belief of the action choice of their opponents. Biases are heterogeneous within the population and unobserved to other players. I show that if one is willing to adopt the ‘indirect evolutionary approach’ of faster growth of preferences that induce relative successful behavior, situations in which no agents hold preferences that are equivalent to material payoffs are stable for (almost all) games in strategic form if a general model is considered. This is contrary to Ok & Vega-Redondo’s (2001) result in a different setup.</p

Modelling religious signalling

The origins of human social cooperation confound simple evolutionary explanation. But from Darwin and Durkheim onwards, theorists (anthropologists and sociologists especially) have posited a potential link with another curious and distinctively human social trait that cries out for explanation: religion. This dissertation explores one contemporary theory of the co-evolution of religion and human social cooperation: the signalling theory of religion, or religious signalling theory (RST). According to the signalling theory, participation in social religion (and its associated rituals and sanctions) acts as an honest signal of one's commitment to a religiously demarcated community and its way of doing things. This signal would allow prosocial individuals to positively assort with one another for mutual advantage, to the exclusion of more exploitative individuals. In effect, the theory offers a way that religion and cooperation might explain one another, but which that stays within an individualist adaptive paradigm. My approach is not to assess the empirical adequacy of the religious signalling explanation or contrast it with other explanations, but rather to deal with the theory in its own terms - isolating and fleshing out its core commitments, explanatory potential, and limitations. The key to this is acknowledging the internal complexities of signalling theory, with respect to the available models of honest signalling and the extent of their fit (or otherwise) with religion as a target system. The method is to take seriously the findings of formal modelling in animal signalling and other disciplines, and to apply these (and methods from the philosophy of biology more generally) to progressively build up a comprehensive picture of the theory, its inherent strengths and weaknesses. The first two chapters outline the dual explanatory problems that cooperation and religion present for evolutionary human science, and surveys contemporary approaches toward explaining them. Chapter three articulates an evolutionary conception of the signalling theory, and chapters four to six make the case for a series of requirements, limitations, and principles of application. Chapters seven and eight argue for the value of formal modelling to further flesh out the theory's commitments and potential and describe some simple simulation results which make progress in this regard. Though the inquiry often problematizes the signalling theory, it also shows that it should not be dismissed outright, and that it makes predictions which are apt for empirical testing