Evaluating information in zero-sum games with incomplete information on both sides

In a Bayesian game some players might receive a noisy signal regarding the specific game actually being played before it starts. We study zero-sum games where each player receives a partial information about his own type and no information about that of the other player and analyze the impact the signals have on the payoffs. It turns out that the functions that evaluate the value of information share two property. The first is Blackwell monotonicity, which means that each player gains from knowing more. The second is concavity on the space of conditional probabilities.Value of information, Blackwell monotonicity, concavity.

Continuity of the value and optimal strategies when common priors change

We show that the value of a zero-sum Bayesian game is a Lipschitz continuous function of the players?common prior belief, with respect to the total variation metric (that induces the topology of setwise convergence on beliefs). This is unlike the case of general Bayesian games, where lower semi-continuity of Bayesian equilibrium payo¤s rests on the convergence of conditional beliefs (Engl (1995), Kajii and Morris (1998)). We also show upper, and approximate lower, semi- continuity of the optimal strategy correspondence with respect to the total variation norm, and discuss approximate lower semi-continuity of the Bayesian equilibrium correspondence in the context of zero-sum games.Zero-Sum Bayesian Games, Common Prior, Value, Optimal Strategies, Upper Semi-Continuity, Lower Approximate Semi- Continuity.

Online Dispute Resolution Through the Lens of Bargaining and Negotiation Theory: Toward an Integrated Model

[Excerpt] In this article we apply negotiation and bargaining theory to the analysis of online dispute resolution. Our principal objective is to develop testable hypotheses based on negotiation theory that can be used in ODR research. We have not conducted the research necessary to test the hypotheses we develop; however, in a later section of the article we suggest a possible methodology for doing so. There is a vast literature on negotiation and bargaining theory. For the purposes of this article, we realized at the outset that we could only use a small part of that literature in developing a model that might be suitable for empirical testing. We decided to use the behavioral theory of negotiation developed by Richard Walton and Robert McKersie, which was initially formulated in the 1960s. This theory has stood the test of time. Initially developed to explain union-management negotiations, it has proven useful in analyzing a wide variety of disputes and conflict situations. In constructing their theory, Walton and McKersie built on the contributions and work of many previous bargaining theorists including economists, sociologists, game theorists, and industrial relations scholars. In this article, we have incorporated a consideration of the foundations on which their theory was based. In the concluding section of the article we discuss briefly how other negotiation and bargaining theories might be applied to the analysis of ODR

Insisting on a Non-Negative Price: Oligopoly, Uncertainty, Welfare, and Multiple Equilibria

I study Cournot competition under incomplete information about demand while assuming that market price must be non-negative for all demand realizations. Although this assumption is very natural, it has only rarely been made in the earlier literature. Yet it has important economic consequences: (1) multiple (symmetric, pure strategy) equilibria can exist, despite the fact that demand and cost are linear; and (2) expected total surplus can be larger when the firms do not know demand than when they do, a result which has important implications for the social desirability of information sharing. The arguments of the paper are relevant also for price competition and for uncertainty about, e.g., cost or the number of firms, and these issues are discussed.Non-negativity constraint, Multiple equilibria, Value of information, Information sharing, Trade associations, Antitrust policy

Imperfect-Recall Abstractions with Bounds in Games

Imperfect-recall abstraction has emerged as the leading paradigm for practical large-scale equilibrium computation in incomplete-information games. However, imperfect-recall abstractions are poorly understood, and only weak algorithm-specific guarantees on solution quality are known. In this paper, we show the first general, algorithm-agnostic, solution quality guarantees for Nash equilibria and approximate self-trembling equilibria computed in imperfect-recall abstractions, when implemented in the original (perfect-recall) game. Our results are for a class of games that generalizes the only previously known class of imperfect-recall abstractions where any results had been obtained. Further, our analysis is tighter in two ways, each of which can lead to an exponential reduction in the solution quality error bound. We then show that for extensive-form games that satisfy certain properties, the problem of computing a bound-minimizing abstraction for a single level of the game reduces to a clustering problem, where the increase in our bound is the distance function. This reduction leads to the first imperfect-recall abstraction algorithm with solution quality bounds. We proceed to show a divide in the class of abstraction problems. If payoffs are at the same scale at all information sets considered for abstraction, the input forms a metric space. Conversely, if this condition is not satisfied, we show that the input does not form a metric space. Finally, we use these results to experimentally investigate the quality of our bound for single-level abstraction

Do market conditions affect gift exchange? Evidence from experimental markets with excess supply and excess demand

We study whether people's behavior in unbalanced gift exchange markets with repeated interaction are affected by whether they are on the excess supply side or the excess demand side of the market. Our analysis is based on the comparison of behavior between two types of experimental gift exchange markets, which vary only with respect to whether first or second movers are on the long side of the market. The direction of market imbalance could influence subjects' behavior, as second movers (workers) might react differently to favorable actions by first movers (firms) in the two cases. While our data show strong deviations from the standard game-theoretic prediction, we find mainly secondary treatment effects. Wage offers are not higher when there is an excess supply of firms, and workers do not respond more favorably to a given wage when there is an excess supply of labor. The state of competition does not appear to have strong effects in our data. We also present data from single-period sessions that show substantial gift exchange even without repeated interactions.

Insisting on a Non-Negative Price: Oligopoly, Uncertainty, Welfare, and Multiple Equilibria

I study Cournot competition under incomplete information about demand while assuming that market price must be non-negative for all demand realizations. Although this assumption is very natural, it has only rarely been made in the earlier literature. Yet it has important economic consequences: (1) multiple (symmetric, pure strategy) equilibria can exist, despite the fact that demand and cost are linear; and (2) expected total surplus can be larger when the firms do not know demand than when they do, a result which has important implications for the social desirability of information sharing. The arguments of the paper are relevant also for price competition and for uncertainty about, e.g., cost or the number of firms, and these issues are discussed.

Insisting on a Non-Negative Price: Oligopoly, Uncertainty, Welfare, and Multiple Equilibria

I study Cournot competition under incomplete information about demand while assuming that market price must be non-negative for all demand realizations. Although this assumption is very natural, it has only rarely been made in the earlier literature. Yet it has important economic consequences: (1) multiple (symmetric, pure strategy) equilibria can exist, despite the fact that demand and cost are linear; and (2) expected total surplus can be larger when the firms do not know demand than when they do, a result which has important implications for the social desirability of information sharing. The arguments of the paper are relevant also for price competition and for uncertainty about, e.g., cost or the number of firms, and these issues are discussed. ZUSAMMENFASSUNG - (Bestehen auf einen nichtnegativen Preis: Oligopol, Ungewißheit, Wohlfahrt und multiple Gleichgewichte) In diesem Beitrag wird Cournot-Wettbewerb bei unvollständiger Information über die Nachfrage untersucht und unterstellt, daß der Marktpreis für alle Realisierungen der Nachfrage nichtnegativ ist. Obgleich diese Annahme sehr selbstverständlich ist, ist sie nur selten in der früheren Literatur verwendet worden. Dennoch hat sie wichtige ökonomische Konsequenzen: (1) können multiple Gleichgewichte existieren (symmetrisch, bei reinen Strategien), obwohl Nachfrage und Kosten linear sind; und (2) kann erwarteter Gesamtüberschuß größer sein, wenn die Unternehmen die Nachfrage nicht kennen als im Falle sie ihnen nicht bekannt ist. Dieses Ergebnis hat wichtige Implikationen für die soziale Erwünschtheit der gemeinsamen Nutung von Information ("Information sharing"). Die Argumente des Beitrags sind auch für Preiskonkurrenz und für Ungewißheit beispielsweise hinsichtlich der Kosten oder der Zahl von Unternehmen relevant. Sie werden abschließend besprochen.Non-negativity constraint, Multiple equilibria, Value of information, Information sharing, Trade associations, Antitrust policy