Incomplete Information Games with Multiple Priors

We present a model of incomplete information games with sets of priors. Upon arrival of private information, each player "updates" by the Bayes rule each of priors in this set to construct the set of posteriors consistent with the arrived piece of information. Then the player uses a possibly proper subset of this set of posteriors to form beliefs about the opponents' strategic choices. And finally the player evaluates his actions by the most pessimistic posterior beliefs `a la Gilboa and Schmeidler (1989). So each player's preferences may exhibit non-linearity in probabilities which can be interpreted as the player's aversion to ambiguity or uncertainty. In this setup, we define a couple of equilibrium concepts, establish existence results for them, and demonstrate by examples how players' views on uncertainty about the environment affect the strategic outcomes.incomplete information games; multiple priors; ambiguity aversion; uncertainty aversion

Distributionally Robust Games with Risk-averse Players

We present a new model of incomplete information games without private information in which the players use a distributionally robust optimization approach to cope with the payoff uncertainty. With some specific restrictions, we show that our "Distributionally Robust Game" constitutes a true generalization of three popular finite games. These are the Complete Information Games, Bayesian Games and Robust Games. Subsequently, we prove that the set of equilibria of an arbitrary distributionally robust game with specified ambiguity set can be computed as the component-wise projection of the solution set of a multi-linear system of equations and inequalities. For special cases of such games we show equivalence to complete information finite games (Nash Games) with the same number of players and same action spaces. Thus, when our game falls within these special cases one can simply solve the corresponding Nash Game. Finally, we demonstrate the applicability of our new model of games and highlight its importance.Comment: 11 pages, 3 figures, Proceedings of 5th the International Conference on Operations Research and Enterprise Systems ({ICORES} 2016), Rome, Italy, February 23-25, 201

Risk and Wealth in a Model of Self-fulfilling Currency Crises

We analyze the effect of risk aversion, wealth and portfolios on the behavior of investors in a global game model of currency crises with continuous action choices. The model generates a rich set of striking theoretical predictions. For example, risk aversion makes currency crises significantly less likely; increased wealth makes crises more likely; and foreign direct investment (illiquid investments in the target currency) make crises more likely. Our results extend linearly to a heterogeneous agent population.Currency crisis, Sunspots, Global games, Risk aversion, Wealth, Portfolio

Risk and Wealth in a Model of Self-fulfilling Currency Crises

Market participants' risk attitudes, wealth and portfolio composition influence their positions in a pegged foreign currency and, therefore, may have important effects on the sustainability of currency pegs. We analyze such effects in a global game model of currency crises with continuous action choices. The model, solved in closed form, generates a rich set of theoretical predictions consistent with many popular and academic (unmodelled) speculations about the onset and timing of currency crises. The results extend linearly to a heterogeneous agent population.Currency crisis, Global games, Risk aversion, Wealth, Portfolio

Bargaining under Incomplete Information, Fairness, and the Hold-Up Problem

In the hold-up problem incomplete contracts cause the proceeds of relation specific investments to be allocated by ex-post bargaining. The present paper investigates the efficiency of incomplete contracts if individuals have heterogeneous preferences implying heterogeneous bargaining behavior and - equally important - preferences are private information. As the sunk investment costs can thus potentially signal preferences, they can influence beliefs and consequently bargaining outcomes. The necessities of signalling are shown to generate very strong investment incentives. These incentives are based on the desire not to reveal information that is unfavorable in the ensuing bargaining. After finding all perfect Bayesian equilibria in pure strategies, the paper derives the necessary and sufficient conditions under which it is optimal to invest and trade efficiently

Dynamic Efficiency, the Riskless Rate, and Debt Ponzi Games under Uncertainty.

In a dynamically efficient economy, can a government roll its debt forever and avoid the need to raise taxes? In a series of examples of economies with zero growth, this paper shows that such Ponzi games may be infeasible even when the average rate of return on bonds is negative, and may be feasible even when the average rate of return on bonds is positive. The paper then reveals the structure which underlies these examples.

Sequential Two-Player Games with Ambiguity

If players' beliefs are strictly non-additive, the Dempster-Shafer updating rule can be used to define beliefs off the equilibrium path. We define an equilibrium concept in sequential two-person games where players update their beliefs with the Dempster-Shafer updating rule. We show that in the limit as uncertainty tends to zero, our equilibrium approximates Bayesian Nash equilibrium by imposing context-dependent constraints on beliefs under uncertainty.

Uncertainty Aversion and Backward Induction

In the context of the centipede game this paper discusses a solution concept for extensive games that is based on subgame perfection and uncertainty aversion. Players who deviate from the equilibrium path are considered non- rational. Rational players who face non-rational opponents face genuine uncertainty and may have non-additive beliefs about their future play. Rational players are boundedly uncertainty averse and maximise Choquet expected utility. It is shown that if the centipede game is sufficiently long, then the equilibrium strategy is to play `Across' early in the game and to play `Down' late in the game.