Communication and equilibrium in discontinuous games of incomplete information

This paper offers a new approach to the study of economic problems usually modeled as games of incomplete information with discontinuous payoffs. Typically, the discontinuities arise from indeterminacies (ties) in the underlying problem. The point of view taken here is that the tie-breaking rules that resolve these indeterminacies should be viewed as part of the solution rather than part of the description of the model. A solution is therefore a tie-breaking rule together with strategies satisfying the usual best-response criterion. When information is incomplete, solutions need not exist; that is, there may be no tie-breaking rule that is compatible with the existence of strategy profiles satisfying the usual best-response criteria. It is shown that the introduction of incentive compatible communication (cheap talk) restores existence

Robustness to Strategic Uncertainty (Revision of DP 2010-70)

We model a player’s uncertainty about other players’ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every player’s strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share.Nash equilibrium;refinement;strategic uncertainty;price competition;Bertrand competition;bargaining;Nash demand game

Dynamic Games with Almost Perfect Information

This paper aims to solve two fundamental problems on finite or infinite horizon dynamic games with perfect or almost perfect information. Under some mild conditions, we prove (1) the existence of subgame-perfect equilibria in general dynamic games with almost perfect information, and (2) the existence of pure-strategy subgame-perfect equilibria in perfect-information dynamic games with uncertainty. Our results go beyond previous works on continuous dynamic games in the sense that public randomization and the continuity requirement on the state variables are not needed. As an illustrative application, a dynamic stochastic oligopoly market with intertemporally dependent payoffs is considered

Endogenous Timing of Moves in Bertrand-Edgeworth Triopolies

We determine the endogenous order of moves in which the firms set their prices in the framework of a capacity-constrained Bertrand-Edgeworth triopoly. A three-period timing game that determines the period in which the firms announce their prices precedes the price-setting stage. We show for the non-trivial case (in which the Bertrand-Edgeworth triopoly has only an equilibrium in non-degenerated mixed-strategies) that the firm with the largest capacity sets its price first, while the two other firms set their prices later. Our result extends a finding by Deneckere and Kovenock (1992) from duopolies to triopolies. This extension was made possible by Hirata's (2009) recent advancements on the mixed-strategy equilibria of Bertrand-Edgeworth games

Endogenous Timing in Pollution Control: Stackelberg versus Cournot-Nash Equilibria

In the framework of international cooperation on climate change to control greenhouse gas emissions (GHG), this paper aims to shed new light on the eventuality of the emergence of a country (or a group of countries) behaving as a leader in the implementation of its environmental policy. The sequence of moves in the existing literature is usually an exogenous assumption, – known as the Cournot assumption (if countries take action simultaneously) and the Stackelberg assumption (if they act sequentially, the latter observing the strategy of the former). The main purpose here is to make the timing endogenous. To do so, we introduce a pre-play stage in the basic two-country game. Then we provide different sets of minimal conditions – on the benefit and damage functions linked to GHG emissions into the atmosphere, yielding respectively the simultaneous and the two sequential modes of play. While the results essentially confirm the prevalence of the former, they also indicate that the latter are natural under some robust conditions: a leader can emerge endogenously when implementing its environmental policy. Finally we provide sufficient conditions for a specific leader to appear. All the results come with an analysis in terms of global emissions and global welfare. No extraneous assumptions such as concavity, existence, or uniqueness of equilibria are needed, and the analysis makes crucial use of the basic results from the theory of supermodular games.Climate change; non cooperative game; global pollution; strategic interactions; endogenous timing; supermodular game theory

Competition between market-making Intermediaries

We introduce capacity constrained competition between market-making intermediaries in a model in which agents can choose between trading with intermediaries, joining a search market or remaining inactive. Recently, market-making by a monopolistic intermediary has been analyzed by Rust and Hall (2003) and Gehrig (1993). Market-makers set publicly observable ask and bid prices. Because market-making involves price setting, without further restrictions competition between market-making intermediaries is Bertrand-like and yields the Walrasian outcome, where the ask-bid spread is zero (Rust and Hall 2003, Gehrig 1993). However, positive ask-bid spreads and competition between market-makers can be observed in reality, e.g. in banking and in retailing. Following Kreps and Scheinkman (1983) and Boccard and Wauthy (2000), we therefore introduce physical capacity constraints. This allows for a gradual transition from monopolistic to perfectly competitive intermediation as the number of intermediaries increases. In particular, we show that given Cournot capacities, intermediaries will set Cournot bid and ask prices in the subsequent subgames, so that the equilibrium of the intermediated market coincides with the Walrasian equilibrium as the number of intermediaries becomes largeMarket-making, capacity constrained competition, market microstructure

A Price-setting Game with a Nonatomic Fringe

This paper extends the Bertrand-Edgeworth price-setting game with finitely many firms to a game with infinitely many firms. Taking a market with one significant firm and a nonatomic fringe, we present a microfoundation of dominant-firm price leadership

A Robust Folk Theorem for the Prisoners' Dilemma

We prove the folk theorem for the Prisoner's dilemma using strategies that are robust to private monitoring. From this follows a limit folk theorem : when players are patient and monitoring is sufficiently accurate, (but private and possibly independent) any feasible individually rational payoff can be obtained in sequential equilibrium. The strategies used can be implemented by finite (randomizing) automata.