Bounded memory and permanent reputations

A recent result in repeated incomplete information games is that after an arbitrarily long history, any equilibrium of the continuation game must be an equilibrium of the complete information game. This result implies that reputation is a short-run phenomenon. We study a particular class of reputation games and show that bounded memory may lead to permanent reputations. In fact, for a particular range of parameters, a bounded memory player may never be able to learn anything at all.     

Die Theorie globaler Spiele: Private Information als Mittel zur Vermeidung multipler Gleichgewichte

Investment decisions with network effects, refinancing illiquid firms, and speculative attacks are typical examples for coordination games with multiple equilibria. By introducing private information about payoff relevant parameters, the theory of global games embeds such coordination games in a stochastic environment, in which the game may have a unique equilibrium. This paper provides an introduction to the theory of global games and shows that it delivers a unique equilibrium if private information is sufficiently precise, while public information may lead to equilibria with self-fulfilling beliefs. This implies some criteria for optimal mechanisms of information dissemination. For example, a well-informed central bank can minimize the prior probability of currency crises by committing to provide information to private actors with small idiosyncratic errors.     

Sequential decisions under uncertainty and the maximum theorem

For sequential decision problems in which the decision-maker observes a process of state variables and chooses an adapted process of action variables, the paper defines a topology on the space of measures of processes of state variables which ensures the applicability of Berge's maximum theorem to the decision-maker's optimal behavior. The topology controls for the information available to the decision-maker at each decision date. The paper also discusses the implications of the analysis for the dynamic-programming approach to sequential decision-making under uncertainty, and for equilibrium existence proof strategies in sequential-market models and games.     

Social pressure,uncertainty, and cooperation

We analyse the role of uncertainty in a sequential game where players have to decide whether to contribute to a public project or not. A player's payoff may depend on his belief about the other player's action which allows us to model social pressure. Using the theory of psychological games, we show that the players' propensity to choose an individually costly action such as cooperation in a public project may increase if there is some uncertainty about who has cooperated before. A central agency, e.g. the government, can induce incomplete information by using a randomization policy, thus crowding in private contributions. Received: November 16, 1998 / Accepted: May 31, 1999     

Solving dynamic public insurance games with endogenous agent distributions: Theory and computational approximation

We make two contributions in this paper. First, we extend the characterization of equilibrium payoff correspondences in history-dependent dynamic policy games to a class with endogenously heterogeneous private agents. In contrast to policy games involving representative agents, this extension has interesting consequences as it implies additional nonlinearity (i.e., bilinearity) between the game states (distributions) and continuation/promised values in the policymaker’s objective and incentive constraints. The second contribution of our paper is in addressing the computational challenges arising from this payoff-relevant nonlinearity. Exploiting the game’s structure, we propose implementable approximate bilinear programming formulations to construct estimates of the equilibrium value correspondence. Our approximation method respects the property of upper hemicontinuity in the target correspondence. We provide small-scale computational examples as proofs of concept.     

An evolutionary game theory model for the inter-relationships between financial regulation and financial innovation

Financial regulation and financial innovation tend to show a dynamic game process of ‘regulation-innovation-re-regulation-re-innovation’. This paper constructs an evolutionary game model to simulate the above phenomena for analyzing the stable equilibrium strategies between financial institutions and regulation institutions. Previous studies mainly stay in a theoretical perspective; instead, this study uses the financial and macroeconomic data of the U.S. during 1947–2007 to numerically demonstrate the dynamic evolution paths of financial regulation and financial innovation. This study finds that the financial regulation and financial innovation of the U.S. presents a dynamic adjustment process by promoting the development of each other. Both regulatory and innovative strategies should be coordinated in the evolutionary progress in a timely and coordinated reason. This study has great referential value for policy makers to balance regulation and innovation in the financial industry and for avoiding financial crises.     

An exact non-cooperative support for the sequential Raiffa solution

This article provides an exact non-cooperative foundation of the sequential Raiffa solution for two-person bargaining games. Based on an approximate foundation due to Myerson (1991) for any two-person bargaining game (S, d) an extensive form game G^S,d is defined that has an infinity of weakly subgame perfect equilibria whose payoff vectors coincide with that of the sequential Raiffa solution of (S, d). Moreover all those equilibria share the same equilibrium path consisting of proposing the Raiffa solution and accepting it in the first stage of the game.By a modification of G^S,d the analogous result is provided for subgame perfect equilibria. These results immediately extend to implementation of a sequential Raiffa (solution based) social choice rule in subgame perfect equilibrium.     

Robust games: theory and application to a Cournot duopoly model

In this paper, the robust game model proposed by Aghassi and Bertsimas (Math Program Ser B 107:231–273, 2006) for matrix games is extended to games with a broader class of payoff functions. This is a distribution-free model of incomplete information for finite games where players adopt a robust-optimization approach to contend with payoff uncertainty. They are called robust players and seek the maximum guaranteed payoff given the strategy of the others. Consistently with this decision criterion, a set of strategies is an equilibrium, robust-optimization equilibrium, if each player’s strategy is a best response to the other player’s strategies, under the worst-case scenarios. The aim of the paper is twofold. In the first part, we provide robust-optimization equilibrium’s existence result for a quite general class of games and we prove that it exists a suitable value \(\epsilon \) such that robust-optimization equilibria are a subset of \(\epsilon \)-Nash equilibria of the nominal version, i.e., without uncertainty, of the robust game. This provides a theoretical motivation for the robust approach, as it provides new insight and a rational agent motivation for \(\epsilon \)-Nash equilibrium. In the last part, we propose an application of the theory to a classical Cournot duopoly model which shows significant differences between the robust game and its nominal version.     

Repeated two-person zero-sum games with unequal discounting and private monitoring

We consider discounted repeated two-person zero-sum games with private monitoring. We show that even when players have different and time-varying discount factors, each player’s payoff is equal to his stage-game minmax payoff in every sequential equilibrium. Furthermore, we show that: (a) in every history on the equilibrium path, the pair formed by each player’s conjecture about his opponent’s action must be a Nash equilibrium of the stage game, and (b) the distribution of action profiles in every period is a correlated equilibrium of the stage game. In the particular case of public strategies in public monitoring games, players must play a Nash equilibrium after any public history.     

Debt contracts and cooperative improvements

In this paper, we consider a dynamic game with imperfect information between a borrower and lender who must write a contract to produce a consumption good. In order to analyze the game, we introduce the concept of a coalitional perfect Bayesian Nash equilibrium (cPBNE). We prove that equilibria exist and are efficient in a precise sense, and that deterministic contracts that resemble debt are optimal for a general class of economies. The cPBNE solution concept captures both the non-cooperative aspect of firm liquidation and the cooperative aspect of renegotiation.     

Pools and streams a stochastic process model of applied research

Applied research is often viewed as a process of testing ideas drawn from a pool of candidate innovations. This model is formalized for the case in which the pool of ideas is continually replenished through basic research. The intensity of applied research is determined by the equilibrium of an n-person non-cooperative game, where players choose dynamic strategies for exploiting the pool. The presence of a pool cannot be detected in a stationary state, but when the number of applied researchers is finite, transient responses to exogenous shifts in basic research policy may reveal the pool's existence.     

Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty

We provide new results for two-stage games in which firms make capacity investments when demand is uncertain, then, when demand is realized, compete in prices. We consider games with demand rationing schemes ranging from efficient to proportional rationing. In all cases, there is a subgame perfect equilibrium outcome coinciding with the outcome of the Cournot game with demand uncertainty if and only if (i) the fluctuation in absolute market size is small relative to the cost of capacity, or (ii) uncertainty is such that with high probability the market demand is very large and with the remaining probability the market demand is extremely small. Otherwise, equilibria involve mixed strategies. Further, we show under efficient rationing that condition (i) is sufficient for the unique equilibrium outcome to be an equilibrium outcome of the Cournot game with demand uncertainty.     

On a theorem of Schmeidler

Over a decade ago D. Schmeidler (1973) introduced a concept of non-cooperative equilibrium for games with a continuum of agents and, under a restriction on the payoff functions, established the existence of an equilibrium in pure strategies. The purpose of this note is to reformalize the model and the equilibrium notion of Schmeidler in terms of distributions rather than measurable functions. We shall see how once the definitions are available we get (pure strategy) equilibrium existence theorems quite effortlessly and under general conditions. A number of remarks contain applications to, among others, incomplete information games.     

Making a match: Combining theory and evidence in policy-oriented macroeconomic modeling

A persistent question in the development of models for macroeconomic policy analysis has been the relative role of economic theory and evidence in their construction. This paper looks at some popular strategies that involve setting up a theoretical or conceptual model (CM) which is transformed to match the data and then made operational for policy analysis. A dynamic general equilibrium model is constructed that is similar to standard CMs. After calibration to UK data it is used to examine the utility of formal econometric methods in assessing the match of the CM to the data and also to evaluate some standard model-building strategies.     

Bounds for best response functions in binary games

This paper studies the identification of best response functions in binary games without making strong parametric assumptions about the payoffs. The best response function gives the utility maximizing response to a decision of the other players. This is analogous to the response function in the treatment-response literature, taking the decision of the other players as the treatment, except that the best response function has additional structure implied by the associated utility maximization problem. Further, the relationship between the data and the best response function is not the same as the relationship between the data and the response function in the treatment-response literature. We focus especially on the case of a complete information entry game with two firms. We also discuss the case of an entry game with many firms, non-entry games, and incomplete information. Our analysis of the entry game is based on the observation of realized entry decisions, which we then link to the best response functions under various assumptions including those concerning the level of rationality of the firms, including the assumption of Nash equilibrium play, the symmetry of the payoffs between firms, and whether mixed strategies are admitted.     

Game-Theoretic Modelling of Transboundary Pollution

Transboundary pollution is pollution which is emitted in one country, and deposited or causing harm in another country. Due to the absence of a supranational institution that could enforce international legislation, transboundary externalities cannot be approached in the same way as domestic pollution problems. In an attempt to find non-traditional solutions to such crossborder problems, recent environmental economics literature incorporates behavioural assumptions with the help of game theory. This paper discusses how different types of transboundary pollution have been approached, and which static and dynamic game theoretic solution concepts have been evaluated. While full cooperation among countries yields the economically optimal outcome it is difficult to reach, because countries are faced with an inequitable sharing of the burden of pollution abatement and with the incentive to free-ride. Side payment schemes to aid burden sharing and strategies to circumvent free riding are reviewed. Issues such as transaction costs, information and motivation are briefly discussed.     

Convergence to Walrasian equilibrium with minimal information

We consider convergence to Walrasian equilibrium in a situation where firms know only market price and their own cost function. We term this a situation of minimal information. We model the problem as a large population game of Cournot competition. The Nash equilibrium of this model is identical to the Walrasian equilibrium. We apply the best response (BR) dynamic as our main evolutionary model. This dynamic can be applied under minimal information as firms need to know only the market price and the their own cost to compute payoffs. We show that the BR dynamic converges globally to Nash equilibrium in an aggregative game like the Cournot model. Hence, it converges globally to the Walrasian equilibrium under minimal information. We extend the result to some other evolutionary dynamics using the method of potential games.

     

A stochastic differential game of capitalism

We develop a stochastic differential game of capitalism to analyze the role of uncertainty. In the deterministic game, the firm’s rent is completely taxed away and the firm stops investing completely. In the stochastic game, the government does not tax the firm’s rent completely. The firm posts a positive rate of investment if the firm’s rent exceeds the labor’s income. Although the cooperative solution is indeterminate, cooperation is always Pareto optimal compared to the non-cooperative Markovian Nash equilibrium. For individual rationality, we apply a payoff distribution procedure based on Yeung and Petrosyan (2006) to derive a subgame-consistent solution.     

Assessing international commonality in macroeconomic uncertainty and its effects

This paper uses a large vector autoregression to measure international macroeconomic uncertainty and its effects on major economies. We provide evidence of significant commonality in macroeconomic volatility, with one common factor driving strong comovement across economies and variables. We measure uncertainty and its effects with a large model in which the error volatilities feature a factor structure containing time-varying global components and idiosyncratic components. Global uncertainty contemporaneously affects both the levels and volatilities of the included variables. Our new estimates of international macroeconomic uncertainty indicate that surprise increases in uncertainty reduce output and stock prices, adversely affect labor market conditions, and in some economies lead to an easing of monetary policy.