Computer Science and Game Theory: A Brief Survey

There has been a remarkable increase in work at the interface of computer science and game theory in the past decade. In this article I survey some of the main themes of work in the area, with a focus on the work in computer science. Given the length constraints, I make no attempt at being comprehensive, especially since other surveys are also available, and a comprehensive survey book will appear shortly.Comment: To appear; Palgrave Dictionary of Economic

A Newton Collocation Method for Solving Dynamic Bargaining Games

We develop and implement a collocation method to solve for an equilibrium in the dynamic legislative bargaining game of Duggan and Kalandrakis (2008). We formulate the collocation equations in a quasi-discrete version of the model, and we show that the collocation equations are locally Lipchitz continuous and directionally differentiable. In numerical experiments, we successfully implement a globally convergent variant of Broyden's method on a preconditioned version of the collocation equations, and the method economizes on computation cost by more than 50% compared to the value iteration method. We rely on a continuity property of the equilibrium set to obtain increasingly precise approximations of solutions to the continuum model. We showcase these techniques with an illustration of the dynamic core convergence theorem of Duggan and Kalandrakis (2008) in a nine-player, two-dimensional model with negative quadratic preferences.

Rational Verification in Iterated Electric Boolean Games

Electric boolean games are compact representations of games where the players have qualitative objectives described by LTL formulae and have limited resources. We study the complexity of several decision problems related to the analysis of rationality in electric boolean games with LTL objectives. In particular, we report that the problem of deciding whether a profile is a Nash equilibrium in an iterated electric boolean game is no harder than in iterated boolean games without resource bounds. We show that it is a PSPACE-complete problem. As a corollary, we obtain that both rational elimination and rational construction of Nash equilibria by a supervising authority are PSPACE-complete problems.Comment: In Proceedings SR 2016, arXiv:1607.0269

Recent developments in empirical IO: dynamic demand and dynamic games

Empirically studying dynamic competition in oligopoly markets requires dealing with large states spaces and tackling difficult computational problems, while handling heterogeneity and multiple equilibria. In this paper, we discuss some of the ways recent work in Industrial Organization has dealt with these challenges. We illustrate problems and proposed solutions using as examples recent work on dynamic demand for differentiated products and on dynamic games of oligopoly competition. Our discussion of dynamic demand focuses on models for storable and durable goods and surveys how researchers have used the "inclusive value" to deal with dimensionality problems and reduce the computational burden. We clarify the assumptions needed for this approach to work, the implications for the treatment of heterogeneity and the different ways it has been used. In our discussion of the econometrics of dynamics games of oligopoly competition, we deal with challenges related to estimation and counterfactual experiments in models with multiple equilibria. We also examine methods for the estimation of models with persistent unobserved heterogeneity in product characteristics, firms’ costs, or local market profitability. Finally, we discuss different approaches to deal with large state spaces in dynamic games.Industrial Organization; Oligopoly competition; Dynamic demand; Dynamic games; Estimation; Counterfactual experiments; Multiple equilibria; Inclusive values; Unobserved heterogeneity.

AN EXAMINATION OF THE STABILITY OF COOPERATION IN A VOLUNTARY COLLECTIVE ACTION: THE CASE OF NONPOINT-SOURCE POLLUTION IN AN AGRICULTURAL WATERSHED

This paper addresses the collective action problem of nonpoint-source pollution control in a small agricultural watershed. At issue is the stability of cooperative behavior among a group of farmers, who have voluntarily agreed to discontinue their use of the herbicide atrazine due to high concentrations of the herbicide in a local water supply. Continued cooperation among the group is threatened by the unexpected cancellation of cyanazine, an inexpensive and widely used alternative to atrazine. With cyanazine no longer available, the farmers will face a significant increase in weed control costs if they continue to use products that do not contain atrazine. Is cooperation among the farmers still possible despite the increased cost of cooperating? This research explores the economic and behavioral factors that influence the collective outcome of this social dilemma. The collective action is modeled as a recurrent coordination problem. The producers (farmers) are engaged in a repeated assurance game with imperfect public information, where producers' choices are driven by the desire to coordinate their actions with the others in the group. A producer's decision to cooperate or defect is based on a threshold approach; if the number of others believed to be cooperating exceeds the level of cooperation required to make cooperation beneficial, then the producer will choose to cooperate. Otherwise, the producer will defect. Since producers are unable to directly observe the choices of the others in the group, each producer must rely on a subjective assessment of the group's behavior based on the realization of the public outcome, the concentration of atrazine in the lake. Producers use a naive Bayesian learning process to update their beliefs about the joint actions of the group. The formal learning process is modeled using a sequential quasi-Bayesian procedure that is consistent with the fictitious play model of learning. The interaction between the producers and the impact of their collective behavior on the levels of atrazine in the lake is formulated as a computational multi-agent system (MAS). The MAS is an artificial representation of the collective action problem that integrates the economic, behavioral and environmental factors that influence the decision-making process of producers. The MAS is used to simulate the evolution of collective behavior among the group and to evaluate the effectiveness of selected incentive mechanisms in preventing the collapse of joint cooperation. The results suggest that without additional incentives, farmers are likely to abandon their voluntary agreement and resume their use of atrazine within the watershed. It is then demonstrated how a combination of policy instruments can be used to alter the underlying game configuration of the collective action problem, resulting in cooperative outcomes. An ambient-based penalty, when used in conjunction with a subsidy payment, is shown to produce divergent incentive structures that shift the classification of the collective action away from a coordination problem with two equilibria to a mixed configuration containing several different game structures and many possible equilibria. This result has important consequences in terms of the evolution of producer behavior and the set of possible collective outcomes. The analysis concludes with an example, which demonstrates that when a mixture of game structures characterizes the collective action, joint cooperation is not a prerequisite to the realization of socially desirable outcomes. By carefully selecting the combination of subsidy payment and ambient penalty, a policy maker can manipulate the underlying structure of the collective action, whereby producers with the smallest impact on water quality choose to defect while all others cooperate.Environmental Economics and Policy,