Secrecy, two-sided bias and the value of evidence

We provide necessary and sufficient conditions on players' preferences for a verifiable message game to possess a separating equilibrium and/or a pooling equilibrium, as well as sufficient conditions for every equilibrium of such a game to be pooling. We also characterize all nonseparating equilibria, and use this property to show that less information might be conveyed in any equilibrium of a verifiable message game than in some equilibrium of the cheap talk game with the same parameters.     

Generalized potentials and robust sets of equilibria

This paper introduces generalized potential functions of complete information games and studies the robustness of sets of equilibria to incomplete information. A set of equilibria of a complete information game is robust if every incomplete information game where payoffs are almost always given by the complete information game has an equilibrium which generates behavior close to some equilibrium in the set. This paper provides sufficient conditions for the robustness of sets of equilibria in terms of argmax sets of generalized potential functions. These sufficient conditions unify and generalize existing sufficient conditions. Our generalization of potential games is useful in other game theoretic problems where potential methods have been applied.     

Endogenous private information structures

We formally incorporate the option to gather information into a game and thus endogenize the information structure. We ask whether models with exogenous information structures are robust with respect to this endogenization. Any Nash equilibrium of the game with information acquisition induces a Nash equilibrium in the corresponding game with an exogenous structure. We provide sufficient conditions on the structure of the game for which this remains true when ‘Nash’ is replaced by ‘sequential’. We characterize the (sequential) Nash equilibria of games with exogenous information structures that can arise as a (sequential) Nash equilibrium of games with endogenous information acquisition.     

Game Theory via Revealed Preferences

We investigate equilibrium notions in game theory from the revealed preference approach. For extensive game forms with complete information, we derive a set of independent necessary and sufficient conditions for the observed outcomes to be rationalized by subgame-perfect Nash equilibrium. Journal of Economic Literature Classification Numbers: C72, C92.     

Auction and the informed seller problem

A seller possessing private information about the quality of a good attempts to sell it through a second-price auction with announced reserve price. The choice of a reserve price transmits information to the buyers. We characterize the equilibria with monotone beliefs of the resulting signaling game and show that they lead to a reduced probability of selling the good compared to the symmetric information situation. We compare the unique separating equilibrium of this signaling game to the equilibrium of a screening game in which an uninformed monopoly broker chooses the trading mechanism. We show that the ex ante expected probability of trade may be larger with a monopoly broker, as well as the ex ante total expected surplus.     

Rational exuberance

We study a two-player investment game with information externalities. Necessary and sufficient conditions for a unique symmetric switching equilibrium are provided. When public news indicates that the investment opportunity is very profitable, too many types are investing early and investments should therefore be taxed. Conversely, any positive investment tax is suboptimally high if the public information is sufficiently unfavorable.     

Existence of nontrivial equilibria in repeated games with imperfect private monitoring

We consider finitely repeated games with imperfect private monitoring, and provide several sufficient conditions for such a game to have an equilibrium whose outcome is different from repetition of Nash equilibria of the stage game. Surprisingly, the conditions are consistent with uniqueness of the stage game equilibrium. A class of repeated chicken is shown to satisfy the condition.     

Bargaining over loan contracts with signaling

This paper combines a sequential bargaining game between an enterprise and a fixed number of banks with a signaling game through which the enterprise reveals her project quality as well as her market-speed on the lending market. We characterize subgame-perfect Nash equilibrium loan contracts that are supported by separating perfect Bayesian equilibria in the signaling game. In contrast to existing models of lending markets, low-quality investment projects might be rewarded with more favorable equilibrium loan contracts than high-quality projects. Also in contrast to existing models, an increase in the competitive pressure between banks reduces the aggregate welfare in our model. The reason is that more favorable loan conditions come with a greater incentive for the ‘strong’ entrepreneur to distinguish herself from her ‘weak’ counterpart through socially wasteful signaling costs.     

创新技术价值信息不对称下厂商的许可策略

本文构建了创新技术商业价值信息不对称情况下在位创新厂商和生产厂商间的技术许可博弈模型,并运用逆向归纳法分别寻求混同均衡和分离均衡。分析结果表明,若运用两部制许可方式,从创新厂商的角度出发,当创新技术高经济价值的可能性较大时,高提成费用混同许可最优;当创新技术低经济价值的可能性较大时,低提成费用混同许可最优。此外,本文还得出固定费用许可条件下的最优许可策略。无论厂商选择何种许可方式,均不存在分离均衡。     

Finitely repeated games with monitoring options

We study finitely repeated games where players can decide whether to monitor the other players? actions or not every period. Monitoring is assumed to be costless and private. We compare our model with the standard one where the players automatically monitor each other. Since monitoring other players never hurts, any equilibrium payoff vector of a standard finitely repeated game is an equilibrium payoff vector of the same game with monitoring options. We show that some finitely repeated games with monitoring options have sequential equilibrium outcomes which cannot be sustained under the standard model, even if the stage game has a unique Nash equilibrium. We also present sufficient conditions for a folk theorem, when the players have a long horizon.     

Information structures and decentralizability of equilibria

Summary Decentralizability with respect to an equilibrium concept means that those equilibria for an extensive game and its agent normal form game coincide for any given payoffs. We consider decentralizability of Nash equilibrium, subgame perfect equilibrium, and perfect equilibrium. For each equilibrium concept we give a necessary and sufficient condition on the information structure of an extensive game for decentralizability to hold. When it holds it does not matter if agents with the same objectives decide independently or have someone coordinate their actions.The author thanks Satish Chand, Mamoru Kaneko, Akira Okada and participants at seminars at the Australian National University, Kyoto University, University of Tsukuba, and The First Decentralization Conference in Japan held at Keio University for valuable suggestions and comments.     

Nash equilibrium when players account for the complexity of their forecasts

Nash equilibrium is often interpreted as a steady state in which each player holds the correct expectations about the other players' behavior and acts rationally. This paper investigates the robustness of this interpretation when there are small costs associated with complicated forecasts. The model consists of a two-person strategic game in which each player chooses a finite machine to implement a strategy in an infinitely repeated 2×2 game with discounting. I analyze the model using a solution concept called Nash Equilibrium with Stable Forecasts (ESF). My main results concern the structure of equilibrium machine pairs. They provide necessary and sufficient conditions on the form of equilibrium strategies and plays. In contrast to the “folk theorem,” these structural properties place severe restrictions on the set of equilibrium paths and payoffs. For example, only sequences of the one-shot Nash equilibrium can be generated by any ESF of the repeated game of chicken.     

Strategic complementarities and search market equilibrium

In this paper, we apply supermodular game theory to the equilibrium search literature with sequential search. We identify necessary and sufficient conditions for the pricing game to exhibit strategic complementarities and prove existence of equilibrium. We then show that price dispersion is inherently incompatible with strategic complementarities in the sense that the Diamond Paradox obtains when firms are identical and is robust within the class of search cost densities that are small near zero and support strategic complementarities. We also show that a major criticism of the literature, that agents act as if they know the distribution of prices, can be justified in the sense of convergent best response dynamics.     

Efficiency and information aggregation in large uniform-price auctions

We prove that the equilibria of a large interdependent-value, uniform-price auction model where bidders have arbitrary preferences for multiple units can be approximated by a nonatomic exchange economy. We show that the uniform-price auction is approximately efficient with a large number of participants and asymptotically aggregates idiosyncratic bidder information into the market price. More generally our analysis framework provides conditions justifying the use of nonatomic limit model approximations to analyze the large-market behavior of game-theoretic models. We demonstrate continuity requirements on the economic primitives sufficient for the equilibrium strategies of the two models to converge as the number of participants in the finite game approaches infinity.     

Campaign Advertising and Voter Welfare

This paper investigates the role of campaign advertising and the opportunity of legal restrictions on it. An electoral race is modelled as a signalling game with three classes of players: many voters, two candidates, and one interest group. The group has non–verifiable insider information on the candidates' quality and, on the basis of this information, offers a contribution to each candidate in exchange for a favourable policy position. Candidates spend the contributions they receive on non–directly informative advertising. This paper shows that: (1) a separating equilibrium exists in which the group contributes to a candidate only if the insider information about that candidate is positive; (2) although voters are fully rational, a ban on campaign advertising can be welfare–improving; and (3) split contributions may arise in equilibrium (and, if they arise too often, they are detrimental to voters).     

Cheap talk with multiple audiences: An experimental analysis

We examine strategic information transmission in a controlled laboratory experiment of a cheap talk game with one sender and multiple receivers. We study the change in equilibrium behavior from the addition of another audience as well as from varying the degree of conflict between the senderʼs and receiversʼ preferences. We find that, as in cheap talk games with just one receiver, information transmission is higher in games with a separating equilibrium, than in games with only a babbling equilibrium. More interestingly, we find clear evidence that the addition of another audience alters the communication between the sender and the receiver in a way consistent with the theoretical predictions. There is evidence of the presence of agents that are systematically truthful as senders and trusting as receivers: deviations from the theoretical predictions, however, tend to disappear with experience, and learning is faster precisely in the games where deviations are more pronounced.     

Comparative statics in a simple class of strategic market games

This paper investigates the effects of entry in two-sided markets where buyers and sellers act strategically. Applying new tools from supermodular optimization/games, sufficient conditions for different comparative statics results are obtained. While normality of one good is sufficient for the equilibrium price to be increasing in the number of buyers, normality of both goods is required for equilibrium bids and sellers' equilibrium utilities to be increasing in the number of buyers. When the economy is replicated, normality of both goods and gross substitutes guarantee that the equilibrium of the strategic market game converges monotonically (in quantities) to the competitive equilibrium. Simple counter-examples are provided to settle other potential conjectures of interest.     

On the existence of pure strategy Nash equilibria in two person discrete games

We construct a generalized two-person discrete strategy static game of complete information where continuity, convexity and compactness cannot be invoked to show the existence of pure strategy Nash equilibrium. We show that, when best responses are unique from both sides, a condition of Minimal Acyclicity is necessary and sufficient for the existence of pure strategy Nash equilibria.     

Game theoretic modeling of increasing returns to scale

This paper surveys the analysis, by means of cooperative game theory, of economies in which there are increasing returns to scale. In the first section necessary and sufficient conditions for the existence of a core of a general equilibrium economy are considered. In the second section, the partial equilibrium approach to increasing returns production, which developed along with the natural monopoly literature, is surveyed. The close relationship between the general equilibrium and partial equilibrium approaches is emphasized.     

STABILITY AND INSTABILITY OF THE COUCRNOT EQUILIBRIUM*

Conditions for the Cournot equilibrium to be locally asymptotically stable or unstable are explored, which are still compatible with the second‐order condition for the optimum. The Cournot equilibrium may not be stable even if the condition owing to Fisher (1961 ), Hahn (1962 ), and Okuguchi (1964 , 1976, 1999 ) is satisfied, which was given as a sufficient condition for the Cournot equilibrium to be stable. However, as long as a game by symmetric players is concerned, the Cournot equilibrium is unstable whenever F‐H‐O condition is not satisfied. In this sense, that F‐H‐O condition is not satisfied is sufficient for the Cournot equilibrium to be unstable.