Supermodular social games

A social game is a generalization of a strategic-form game, in which not only the payoff of each player depends upon the strategies chosen by their opponents, but also their set of admissible strategies. Debreu (1952) proves the existence of a Nash equilibrium in social games with continuous strategy spaces. Recently, Polowczuk and Radzik (2004) have proposed a discrete counterpart of Debreu's theorem for two-person social games satisfying some ``convexity properties'. In this note, we define the class of supermodular social games and give an existence theorem for this class of games.Strategic-form games, social games, supermodularity, Nash equilibrium, existence.

Group formation and governance

This paper studies the impact of the governance of a group, whether be it unanimity, simple majority or qualified majority, on its (endogenously derived) size, composition, and inclination to change the status quo. Somewhat surprisingly, we show that not only unanimity might favor the formation of larger groups than majority, but also a change of status quo.groups; endogenous formation; economies of scale; loss of control; governance; unanimity; majority

Supermodular Social Games

A social game is a generalization of a strategic-form game, in which not only the payoff of each player depends upon the strategies chosen by their opponents, but also their set of admissible strategies. Debreu (1952) proves the existence of a Nash equilibrium in social games with continuous strategy spaces. Recently, Polowczuk and Radzik (2004) have proposed a discrete counterpart of Debreu's theorem for two-person social games satisfying some ''convexity properties''. In this note, we define the class of supermodular social games and give an existence theorem for this class of games.strategic-form games, social games, supermodularity, Nash equilibrium, existence

Partnerships

This paper analyzes the endogenous formation of a partnership as the trade-off between efficiency gains and a 'cost' associated with the partial loss of control over the decisions the partnership takes. For instance, by forming a monetary union, countries benefit from a more coordinated monetary policy. However, due to the partial loss of control over the union decision, the policy implemented might differ from the policy a member would have taken on their own. We interpret this possible difference as a cost. We notably show that individuals with ''similar" characteristics form a partnership, and the more diverse the characteristics, the smaller the partnership size.partnerships, coalitions, alliances, endogenous formation, efficiency gains, loss of control, diverse characteristics, opinions

Group formation and governance

This paper studies the impact of the governance of a group, whether be it unanimity, simple majority or qualified majority, on its size, composition, and inclination to change the status quo. Somewhat surprisingly, we show that not only unanimity might favor the formation of larger groups than majority, but also a change of status quo. This paper therefore suggests that unanimity, often blamed for the European inertia of the last two decades, was only a scapegoat.groups; coalitions; alliances; endogenous formation; cost reduction; loss of control; governance; unanimity; majority

Implementation in mixed Nash equilibrium

A mechanism implements a social choice correspondence f in mixed Nash equilibrium if at any preference profile, the set of all pure and mixed Nash equilibrium outcomes coincides with the set of f-optimal alternatives at that preference profile. This definition generalizes Maskin’s definition of Nash implementation in that it does not require each optimal alternative to be the outcome of a pure Nash equilibrium. We show that the condition of weak set-monotonicity, a weakening of Maskin’s monotonicity, is necessary for implementation. We provide sufficient conditions for implementation and show that important social choice correspondences that are not Maskin monotonic can be implemented in mixed Nash equilibrium

Mechanism Design and Communication Networks

This paper characterizes the class of communication networks for which, in any environment (utilities and beliefs), every incentive-compatible social choice function is (partially) implementable. Among others, in environments with either common and independent beliefs and private values or a bad outcome, we show that if the communication network is 2-connected, then any incentive-compatible social choice function is implementable. A network is 2-connected if each player is either directly connected to the designer or indirectly connected to the designer through at least two disjoint paths. We couple encryption techniques together with appropriate incentives to secure the transmission of each player’s private information to the designer.Mechanism design; incentives; Bayesian equilibrium; communication networks; encryption; secure transmission; coding

Debt Contracts with ex-ante and ex-post Asymmetric Information: An Example

We consider a simple model of lending and borrowing combining two informational problems: adverse selection and costly state verification. Our analysis highlights the interaction between these two informational problems. We notably show that the higher the monitoring cost, the less discriminating the optimal menu of contracts is.debt contracts, diversity of opinions, screening, costly monitoring, pooling

Debt contracts with ex-ante and ex-post asymmetric information: an example.

We consider a simple model of lending and borrowing combining two informational problems: adverse selection and costly state verification. Our analysis highlights the interaction between these two informational problems. We notably show that the higher the monitoring cost, the less discriminating the optimal menu of contracts is.Debt contracts; Diversity of opinions; Screening; Costly monitoring; Pooling;

Minimax regret and strategic uncertainty

This paper introduces a new solution concept, a minimax regret equilibrium, which allows for the possibility that players are uncertain about the rationality and conjectures of their opponents. We provide several applications of our concept. In particular, we consider pricesetting environments and show that optimal pricing policy follows a non-degenerate distribution. The induced price dispersion is consistent with experimental and empirical observations (Baye and Morgan (2004)).Minimax regret, rationality, conjectures, price dispersion, auction