Roger Lagunoff

Asynchronous Choice in Repeated Coordination Games

The standard model of repeated games assumes perfect synchronization in the timing of decisions between the players. In many natural settings, however, choices are made synchronously so that only one player can move at a given time. This paper studies a family of repeated settings in which choices are asynchronous. Initially, we examine, as a canonical model, a simple two person alternating move game of pure coordination. There, it is shown that for sufficient patient players, there is a unique perfect equilibrium payoff which Pareto dominates all other payoffs. The result generalizes to any finite number of players and any game in a class of asynchronously repeated games which includes both stochastic and deterministic repetition. The result complement a recent Folk Theorem by Dutta (1995) for stochastic games which can be applied to asynchronously repeated games if a full dimensionality condition holds. A critical feature of the model is the inertia in decisions. We show how the inertia in asynchronous decisions determines the set of equilibrium payoffs.

Financial Fragility with Rational And Irrational Exuberance

This article formalizes investor rationality and irrationality, exuberance and apprehension, to consider the implications of belief formation for the fragility of an economys financial structure. The model presented generates a financial structure with portfolio linkages that make it susceptible to contagious financial crises, despite the absence of coordination failures. Investors forecast the likelihood of loss from contagion and may shift preemptively to safer portfolios, breaking portfolio linkages in the process. The entire financial structure collapses when the last group of investors reallocates their portfolios. If some investors are irrationally exuberant, the financial structure remains intact longer. In fact, financial collapse occurs sooner when almost all investors are rationally exuberant than when they are irrationally exuberant. Additionally, a financial crisis initiated by real shocks is indistinguishable from one caused solely by the presence of rationally apprehensive investors in a fundamentally sound economy. Policies that make portfolio linkages more resilient can improve welfare.

Organizations and Overlapping Generations Games: Memory, Communication, and Altruism

This paper studies the role of memory and communication in overlapping generations (OLG) games between ongoing organizations. In each organization, each individual, upon entry into the game, replaces his predecessor who has the same preferences and faces the same strategic possibilities. An individual has no prior memory - that is, he does not directly witness the events that occur before his tenure. Instead, each individual relies on information about the past from his predecessor via cheap talk. This paper highlights the role of communication as a surrogate for memory. It has been shown elsewhere that Folk Theorems hold in OLG games with long enough lived individuals who can perfectly observe the past. However, the Folk Theorem fails for many games when individuals have no prior memory. We show that for OLG games without prior memory but with costly communication, a Folk Theorem holds only when there is some altruistic link between cohorts in an organization. Our main result asserts that if communication costs are sufficiently small, or if altruistic weights on successors are sufficiently large, then a strongly stationary Folk Theorem (i.e., equilibrium payoffs are time invariant) obtains if a manager’s message is public information. The equilibria in this Folk Theorem require a special form of intergenerational sanctions. In these sanctions, punishment is sometimes carried out long after both victim and perpetrator have left the game. Without this special structure, altruism may in fact destroy cooperation when it would otherwise be possible. Copyright Springer-Verlag Berlin/Heidelberg 2004

Communication in dynastic repeated games: ‘Whitewashes’ and ‘coverups’

Summary.We ask whether communication can directly substitute for memory in dynastic repeated games in which short lived individuals care about the utility of their offspring who replace them in an infinitely repeated game. Each individual is unable to observe what happens before his entry in the game. Past information is therefore conveyed from one cohort to the next by means of communication.When communication is costless and messages are sent simultaneously, communication mechanisms or protocols exist that sustain the same set of equilibrium payoffs as in the standard repeated game. When communication is costless but sequential, the incentives to “whitewash” the unobservable past history of play become pervasive. These incentives to whitewash can only be countered if some player serves as a “neutral historian” who verifies the truthfulness of others’ reports while remaining indifferent in the process. By contrast, when communication is sequential and (lexicographically) costly, all protocols admit only equilibria that sustain stage Nash equilibrium payoffs.We also analyze a centralized communication protocol in which history leaves a “footprint” that can only hidden by the current cohort by a unanimous “coverup.” We show that in this case the set of payoffs that are sustainable in equilibrium coincides with the weakly renegotiation proof payoffs of the standard repeated game.

Communication in Dynastic Repeated Games: 'Whitewashes' and 'Coverups'

We ask whether communication can directly substitute for memory in dynastic repeated games in which short lived individuals care about the utility of their offspring who replace them in an infinitely repeated game. Each individual is unable to observe what happens before his entry in the game. Past information is therefore conveyed from one cohort to the next by means of communication.

Organizations and overlapping generations games: Memory, communication, and altruism

Abstract.This paper studies the role of memory and communication in overlapping generations (OLG) games between ongoing organizations. In each organization, each individual, upon entry into the game, replaces his predecessor who has the same preferences and faces the same strategic possibilities. An individual has no prior memory - that is, he does not directly witness the events that occur before his tenure. Instead, each individual relies on information about the past from his predecessor via cheap talk. This paper highlights the role of communication as a surrogate for memory.It has been shown elsewhere that Folk Theorems hold in OLG games with long enough lived individuals who can perfectly observe the past. However, the Folk Theorem fails for many games when individuals have no prior memory. We show that for OLG games without prior memory but with costly communication, a Folk Theorem holds only when there is some altruistic link between cohorts in an organization. Our main result asserts that if communication costs are sufficiently small, or if altruistic weights on successors are sufficiently large, then a strongly stationary Folk Theorem (i.e., equilibrium payoffs are time invariant) obtains if a manager’s message is public information. The equilibria in this Folk Theorem require a special form of intergenerational sanctions. In these sanctions, punishment is sometimes carried out long after both victim and perpetrator have left the game. Without this special structure, altruism may in fact destroy cooperation when it would otherwise be possible.

Fully Endogenous Mechanism Selection on Finite Outcome Sets

SummaryThis paper defines a choice process over social outcomes in which agents choose the institutional rules ormechanisms themselves without outside interference. Truly “endogenizing” the mechanism selection process in this way, however, involves facing an infinite regress problem in which outcomes are chosen by games which are themselves chosen by games, ad infinitum. This paper allows the possibility of such an infinite regress which we callfully endogenous mechanism selection.We introduce the notion ofFree Choice which restricts the class of mechanisms in the regress to those which prevent agents from being “locked in” to an equilibrium outcome by the actions of others. Under this condition, the infinite regress is shown to get truncated with the number of selection “iterations” endogenously determined. It turns out that the outcomes resulting from a Free Choice-constrained regress are (Weakly) Pareto optimal; in particular, these outcomes solve a weighted “Rawlsian” Maxmin criterion. We also show that these outcomes are invariant to the equilibrium concept used to evaluate games in the regress.

Evolution in mechanisms for public projects

SummaryThis paper considers the explicit, real time dynamic processes in which cooperation emerges in a class ofbinary decision mechanisms, each of which determines funding for a public project. This class includes the Voluntary Contribution and the Majority Voting mechanisms. The population is subject to “turnover” so that new individuals enter society with possibly different beliefs about the future evolution of societal behavior than their predecessors. Individuals in this society maximize their discounted expected utilities. Due to the frequent turnover, however, these expectations may not be mutually consistent. Nevertheless, we find, for each mechanism, the nonempty set of the parameters for which the behavior pattern starting from states with nonprovision is absorbed into states with full provision with probability one. Moreover, for a sufficiently large population, outcomes with full provision are absorbing states if and only if certain types of voting mechanisms are used.

Specialization, inequality and the social stability of economies with collective property rights

Abstract Many, if not most, economies are observed to exhibit some form of collective ownership with some goods. These economies may fail to be socially stable, in the sense that the economy has an empty core; some groups may have an incentive to ‘recontract out’. We show that, for a class of economies with collective ownership, sufficient ‘specialization’ in the endowment holdings of these economies gives rise to a non-empty core, so achieving social stability. It is shown, moreover, that reductions in income inequality are consistent with social stability, to the extent that these reductions preserve or increase ‘specialization’ in the economy. Finally, we show that our notion of specialization is not limited to the privatized sector of the economy. Even in economies in which there is no privately held property, sufficient specialization guarantees that the economy is socially stable.

Are "Anti-Folk Theorems" in Repeated Games Nongeneric?

Folk Theorems in repeated games hold fixed the game payoffs, while the discount factor is varied freely. We show that these results may be sensitive to the order of limits in situations where players move asynchronously. Specifically, we show that when moves are asynchronous, then for a fixed discount factor close to one there is an open neighborhood of games which contains a pure coordination game such that every Perfect equilibrium of every game in the neighborhood approximates to an arbitrary degree the unique Pareto dominant payoff of the pure coordination game.