Asymptotically Truthful Equilibrium Selection in Large Congestion Games

Studying games in the complete information model makes them analytically tractable. However, large $n$ player interactions are more realistically modeled as games of incomplete information, where players may know little to nothing about the types of other players. Unfortunately, games in incomplete information settings lose many of the nice properties of complete information games: the quality of equilibria can become worse, the equilibria lose their ex-post properties, and coordinating on an equilibrium becomes even more difficult. Because of these problems, we would like to study games of incomplete information, but still implement equilibria of the complete information game induced by the (unknown) realized player types. This problem was recently studied by Kearns et al. and solved in large games by means of introducing a weak mediator: their mediator took as input reported types of players, and output suggested actions which formed a correlated equilibrium of the underlying game. Players had the option to play independently of the mediator, or ignore its suggestions, but crucially, if they decided to opt-in to the mediator, they did not have the power to lie about their type. In this paper, we rectify this deficiency in the setting of large congestion games. We give, in a sense, the weakest possible mediator: it cannot enforce participation, verify types, or enforce its suggestions. Moreover, our mediator implements a Nash equilibrium of the complete information game. We show that it is an (asymptotic) ex-post equilibrium of the incomplete information game for all players to use the mediator honestly, and that when they do so, they end up playing an approximate Nash equilibrium of the induced complete information game. In particular, truthful use of the mediator is a Bayes-Nash equilibrium in any Bayesian game for any prior.Comment: The conference version of this paper appeared in EC 2014. This manuscript has been merged and subsumed by the preprint "Robust Mediators in Large Games": http://arxiv.org/abs/1512.0269

Lossy Channel Games under Incomplete Information

In this paper we investigate lossy channel games under incomplete information, where two players operate on a finite set of unbounded FIFO channels and one player, representing a system component under consideration operates under incomplete information, while the other player, representing the component's environment is allowed to lose messages from the channels. We argue that these games are a suitable model for synthesis of communication protocols where processes communicate over unreliable channels. We show that in the case of finite message alphabets, games with safety and reachability winning conditions are decidable and finite-state observation-based strategies for the component can be effectively computed. Undecidability for (weak) parity objectives follows from the undecidability of (weak) parity perfect information games where only one player can lose messages.Comment: In Proceedings SR 2013, arXiv:1303.007

A probabilistic representation for the value of zero-sum differential games with incomplete information on both sides

We prove that for a class of zero-sum differential games with incomplete information on both sides, the value admits a probabilistic representation as the value of a zero-sum stochastic differential game with complete information, where both players control a continuous martingale. A similar representation as a control problem over discontinuous martingales was known for games with incomplete information on one side (see Cardaliaguet-Rainer [8]), and our result is a continuous-time analog of the so called splitting-game introduced in Laraki [20] and Sorin [27] in order to analyze discrete-time models. It was proved by Cardaliaguet [4, 5] that the value of the games we consider is the unique solution of some Hamilton-Jacobi equation with convexity constraints. Our result provides therefore a new probabilistic representation for solutions of Hamilton-Jacobi equations with convexity constraints as values of stochastic differential games with unbounded control spaces and unbounded volatility

Essays on Dynamic Games of Incomplete Information

This dissertation consists of three essays that study the dynamic games with incomplete information. In the first chapter, I study a dynamic trading game where a seller and potential buyers start out symmetrically uninformed about the quality of a good, but the seller becomes informed about the quality, so that the asymmetric information between the agents increases over time. The introduction of a widening information gap results in several new phenomena. In particular, the interaction between screening and learning generates nonmonotonic price and trading patterns, contrary to the standard models in which asymmetric information is initially given. If the seller\u27s effective learning speed is high, the equilibrium features collapse-and-recovery behavior: Both the equilibrium price and the probability of a trade drop at a threshold time and then increase later. The seller\u27s payoff is nonmonotonic in his learning speed, as a slower learning speed can lead to higher payoff for the seller. In the second chapter, I study a dynamic one-sided-offer bargaining model between a seller and a buyer under incomplete information. The seller knows the quality of his product while the buyer does not. During bargaining, the seller randomly receives an outside option, the value of which depends on the hidden quality. If the outside option is sufficiently important, there is an equilibrium in which the uninformed buyer fails to learn the quality and continues to make the same randomized offer throughout the bargaining process. As a result, the equilibrium behavior produces an outcome path that resembles the outcome of a bargaining deadlock and its resolution. The equilibrium with deadlock has inefficient outcomes such as a delay in reaching an agreement and a breakdown in negotiations. Bargaining inefficiencies do not vanish even with frequent offers, and they may exist when there is no static adverse selection problem. In the third chapter, I address the following question: when does an incumbent party have an incentive to experiment with a risky reform policy in the presence of future elections? I study a continuous-time game between two political parties with heterogeneous preferences and a median voter. I show that while infrequent elections are surely bad for the median voter, too frequent elections can also make him strictly worse off. When the election frequency is low, a standard agency problem arises and the incumbent party experiments with its preferred reform policy even if its outlook is not promising. On the other hand, when the election frequency is too high, in equilibrium the incumbent stops experimentation too early because the imminent election increases the incumbent\u27s potential loss of power if it undertakes risky reform. The degree of inefficiency is large enough that too frequent elections are worse for the median voter than a dictatorship

Duality and optimal strategies in the finitely repeated zero-sum games with incomplete information on both sides

The recursive formula for the value of the zero-sum repeated games with incomplete information on both sides is known for a long time. As it is explained in the paper, the usual proof of this formula is in a sense non constructive : it just claims that the players are unable to guarantee a better payoff than the one prescribed by formula, but it does not indicates how the players can guarantee this amount. In this paper we aim to give a constructive approach to this formula using duality techniques. This will allow us to recursively describe the optimal strategies in those games and to apply these results to games with infinite action spaces.Repeated games, dual games, incomplete information, recurrence formula.

Using or Hiding Private Information ? An Experimental Study of Zero-Sum Repeated Games with Incomplete Information

This paper studies experimentally the value of private information in strictly competitive interactions with asymmetric information. We implement in the laboratory three examples from the class of zero-sum repeated games with incomplete information on one side and perfect monitoring. The stage games share the same simple structure, but differ markedly on how information should be optimally used once they are repeated. Despite the complexity of the optimal strategies, the empirical value of information coincides with the theoretical prediction in most instances. In particular, it is never negative, it decreases with the number of repetitions, and it is nicely bounded below by the value of the infinitely repeated game and above by the value of the one-shot game. Subjects are unable to completely ignore their information when it is optimal to do so, but the use of information in the lab reacts qualitatively well to the type and length of the game being played.Concavification, laboratory experiments, incomplete information, value of information, zero-sum repeated games.

Sequential bargaining with pure common values and incomplete information on both sides

We study the alternating-offer bargaining problem of sharing a common value pie under incomplete information on both sides and no depreciation between two identical players. We characterise the essentially unique perfect Bayesian equilibrium of this game which turns out to be in gradually increasing offers.Gradual bargaining; Common values; Incomplete information; Repeated games