All-stage strong correlated equilibrium

A strong correlated equilibrium is a correlated strategy profile that is immune to joint deviations. Different notions of strong correlated equilibria have been defined in the literature. One major difference among those definitions is the stage in which coalitions can plan a joint deviation: before (ex-ante) or after (ex-post) the deviating players receive their part of the correlated profile. In this note we show that an ex-ante strong correlated equilibrium (Moreno D., Wooders J., 1996. Games Econ. Behav. 17, 80-113) is immune to deviations at all stages of any pre-play signalling process that implements it. Thus the set of ex-ante strong correlated equilibria is included in all other sets of strong correlated equilibria

All-stage strong correlated equilibrium

A strong correlated equilibrium is a correlated strategy profile that is immune to joint deviations. Different notions of strong correlated equilibria have been defined in the literature. One major difference among those definitions is the stage in which coalitions can plan a joint deviation: before (ex-ante) or after (ex-post) the deviating players receive their part of the correlated profile. In this note we show that an ex-ante strong correlated equilibrium (Moreno D., Wooders J., 1996. Games Econ. Behav. 17, 80-113) is immune to deviations at all stages of any pre-play signalling process that implements it. Thus the set of ex-ante strong correlated equilibria is included in all other sets of strong correlated equilibria

Ex-ante and ex-post strong correlated equilbrium

A strong correlated equilibrium is a strategy profile that is immune to joint deviations. Different notions of strong correlated equilibria were defined in the literature. One major difference among those definitions is the stage in which coalitions can plan a joint deviation: before (ex-ante) or after (ex-post) the deviating players receive their part of the correlated profile. In this paper we prove that if deviating coalitions are allowed to use new correlating devices, then an ex-ante strong correlated equilibrium is also immune to deviations at the ex-post stage. Thus the set of ex-ante strong correlated equilibria of Moreno & Wooders (1996) is included in all other sets of strong correlated equilibria

All-Stage strong correlated equilbrium

Abstract A strong correlated equilibrium is a strategy profile that is immune to joint deviations. Different notions of strong correlated equilibria were defined in the literature. One major difference among those definitions is the stage in which coalitions can plan a joint deviation: before (ex-ante) or after (ex-post) the deviating players receive their part of the correlated profile. In this paper we show that an ex-ante strong correlated equilibrium is immune to deviations at all stages. Thus the set of ex-ante strong correlated equilibria of Moreno & Wooders (Games Econ. Behav. 17 (1996), 80-113) is included in all other sets of strong correlated equilibria

Correlated equilibria, incomplete information and coalitional deviations

This paper proposes new concepts of strong and coalition-proof correlated equilibria where agents form coalitions at the interim stage and share information about their recommendations in a credible way. When players deviate at the interim stage, coalition-proof correlated equilibria may fail to exist for two-player games. However, coalition-proof correlated equilibria always exist in dominance-solvable games and in games with positive externalities and binary actions

Essays on the All-Pay Auction

Three all-pay auction models are examined. The first is a symmetric two-player binary-signal all-pay auction with correlated signals and interdependent valuations. The first chapter provides a complete characterization of each form of equilibrium and gives conditions for their existence. The main finding is that there generically exists a unique equilibrium. The unique equilibrium can only be one of four forms of equilibria. I apply my all-pay auction model to elections, where a candidate that receives good news from the polls behaves in a rationally overconfident manner and reduces her equilibrium effort. Consequently, the other candidate can win the election in an upset. The second chapter extends Chapter 1\u27s model to N signals. In comparison, the binary model allows for a guess-verify approach. However, the number of possible guesses increases rapidly when N increases. Hence such an approach is infeasible. Chapter 2\u27s approach is centered around linear algebra techniques and a novel notion of a weakly monotone equilibrium. In a weakly monotone equilibrium the bid supports are ordered by the strong set order but not necessarily separated like the traditional monotone equilibrium. I classify these weakly monotone equilibria into four primary forms. I characterize each form and find sufficient conditions for their existence. Furthermore, for the model used in Rentschler and Turocy (2016), I provide a novel necessary and sufficient condition for the existence of a traditional monotone equilibrium. The third chapter considers a two-stage game: a negotiation stage followed by a conflict stage in case the negotiations break down. In a setting with multi-dimensional correlated types, two players compete over a good that is of uncertain but common value. Conflict is modeled as an all-pay auction, which endogenizes the cost of conflict. In the literature, which assumes independent private values or costs, a peaceful equilibrium, in which war occurs with zero probability need not exist. I find that in my correlated pure common-value model, a peaceful equilibrium always exists and is essentially unique. Further, I show that adding private values to this model worsens the prospect of peace, and conflict might occur

Coalition-proof equilibrium

We characterize the set of agreements that the players of a non-cooperative game may reach when they have the opportunity to communicate prior to play. We show that communication allows the players to correlate their actions. Therefore, we take the set of correlated strategies as the space of agreements. Since we consider situations where agreements are non-binding, they must not be subject to profitable self-enforcing deviations by coalitions of players. A coalition-proof equilibrium is a correlated strategy from which no coalition has an improving and self-enforcing deviation. A coalition-proof equilibrium exists when there is a correlated strategy which (i) has a support contained in the set of actions that survive the iterated elimination of strictly dominated strategies, and (ii) weakly Pareto dominates every other correlated strategy whose support is contained in that set. Consequently, the unique equilibrium of a dominance solvable game is coalition-proof

Coalition-proof equilibrium

We characterize the agreements that the players of a noncooperative game may reach when they can communicate prior to play, but they cannot reach binding agreements: A coalition-proo[ equilibrium is a correlated strategy from which no coalition has an improving and self-enforcing deviation. We show that any correlated strategy whose support is contained in the set of actions that survive the iterated elimination of strictly dominated strategies and weakly Pareto dominates every other correlated strategy whose support is contained in that set, is a coalition-proof equilibrium. Consequently, the unique equilibrium of a dominance solvable game is coalition-proof.Publicad

Correlated Equilibria, Incomplete Information and Coalitional Deviations

This paper proposes new concepts of strong and coalition-proof correlated equilibria where agents form coalitions at the interim stage and share information about their recommendations in a credible way. When players deviate at the interim stage, coalition-proof correlated equilibria may fail to exist for two-player games. However, coalition- proof correlated equilibria always exist in dominance-solvable games and in games with positive externalities and binary actions.correlated equilibrium ; coalitions ; information sharing ; games with positive externalities