Core-stable rings in auctions with independent private values

We propose a semi-cooperative game theoretic approach to check whether a given coalition is stable in a Bayesian game with independent private values. The ex ante expected utilities of coalitions, at an incentive compatible (noncooperative) coalitional equilibrium, describe a (cooperative) partition form game. A coalition is core-stable if the core of a suitable characteristic function, derived from the partition form game, is not empty. As an application, we study collusion in auctions in which the bidders? final utility possibly depends on the winner?s identity. We show that such direct externalities offer a possible explanation for cartels? structures (not) observed in practice.     

Proper belief revision and equilibrium in dynamic games

We present a theory of rationality in dynamic games in which players, during the course of the game, may revise their beliefs about the opponents’ utility functions. The theory is based upon the following three principles: (1) the players’ initial beliefs about the opponents’ utilities should agree on some profile u of utility functions, (2) every player should believe, at each of his information sets, that his opponents are carrying out optimal strategies and (3) a player at information set h should not change his belief about an opponent's ranking of strategies a and b if both a and b could have led to h. Scenarios with these properties are called preference conjecture equilibria for the profile u of utility functions. We show that every normal form proper equilibrium for u induces a preference conjecture equilibrium for u, thus implying existence of preference conjecture equilibrium.     

Coalition formation as a dynamic process

We study coalition formation as an ongoing, dynamic process, with payoffs generated as coalitions form, disintegrate, or regroup. A process of coalition formation (PCF) is an equilibrium if a coalitional move to some other state can be “justified” by the expectation of higher future value, compared to inaction. This future value, in turn, is endogenous: it depends on coalitional movements at each node. We study existence of equilibrium PCFs. We connect deterministic equilibrium PCFs with unique absorbing state to the core, and equilibrium PCFs with multiple absorbing states to the largest consistent set. In addition, we study cyclical as well as stochastic equilibrium PCFs.     

Nonpaternalistic intergenerational altruism

The paper develops a concept of equilibrium behaviour and establishes its existence in a model of nonpaternalistic intergenerational altruism. Each generation derives utility from its own consumption and the utilities of its successors. Equilibrium capital stocks are time-monotone and therefore converge to a steady state. Finally. when each generation's utility depends on that of at least two successors, equilibria may be inefficient. This is shown by an example, where feasible programs exist providing greater consumption (compared to the equilibrium path) for every generation.     

Service Quality,Competition, and Regulatory Policies in the Postal Sector

This paper presents a simple model which illustrates the possible policy- and welfare-implications of endogenous product selection in the postal sector. The cost of a unit of mail depends on its "quality" (e.g., speed of delivery) and on the type and location of the addressee (firms, urban households, and rural households). Senders have inelastic demands and differ in their willingness to pay for quality. Addressees are passive but their utility may affect social welfare. Two operators play a two-stage game, first choosing qualities and then prices. We first show that the equilibrium with two private (profit maximizing) operators results in an inefficient provision of quality. Then, we consider the mixed (Nash) equilibrium with one private and one (welfare maximizing) public operator. If the budget constraint of the public firm is not binding, this equilibrium is shown to be first-best efficient even if social welfare accounts for the utility of addressees. If the budget constraint is binding, the mixed equilibrium is not efficient but yields a higher level of welfare than the private equilibrium. Finally, we study the impact of minimum quality standards within our setting.     

Stability when mobility is restricted by the existing coalition structure

In many social and economic situations the optimal solution requires the formation of coalitions that partition the set of players. When the individual player is small relative to the size of the existing coalitions, it seems realistic to assume that the prevailing coalition structure dictates the set of possible blocking coalitions. Specifically, it is assumed that an individual does not consider forming any coalition, but rather joining an already existing one. Two solution concepts for these games are investigated: structural equilibrium and stable payoffs, which are derived from the application of ψ-stability to the core and to the bargaining set, respectively. To this end an extension of the bargaining set to games without side payments is offered. Both solution concepts are shown to exist for some coalition structure. However, while structural equilibrium may fail to exist for any non trivial coalition structure, for every coalition structure there exists a stable payoff.     

Cores,aggressiveness and the breakdown of cooperation in economic games

The paper develops the use of the core as a solution concept in game theory in two interrelated directions. In the first place, an indicator of aggressiveness of claims is introduced in a modified definition of the core. The modified core may be smaller than the usual core, and may fail to exist if aggressiveness increases beyond some critical level. In the second place the article gives a formulation of a mixed cooperative/non-cooperative game, in which the game will be played cooperatively within coalitions, but non-cooperatively as between coalitions. A mixed cooperative/non-cooperative solution obtains if the grand coalition of all players fail to materialize because the various claims are incompatible. The two directions referred to are interrelated because the level of aggressiveness may be decisive for whether or not the grand coalition, and possibly other coalitions, will break down. The final section of the paper draws some general conclusions and relates the approach to other ideas in the literature.     

Power Structure and Rent Competition

This paper presents a model of rent competition in a mixed economic system in which wealth maximizing interest group coalitions share wealth according to their relative political power. The model solves for optimal lobbying expenditures of a producer group, a consumer group, and individual firms. The existence of monopolistic rent is not presupposed. Instead, the equilibrium market price, output, and market shares of firms are determined endogenously. As a result, the distribution of rent depends upon the relative political power of each interest group coalition and total lobbying expenditure decreases as the asymmetry in marginal political power among interest group coalitions increases.     

Valuations and dynamics of negotiations

This paper analyzes three‐party negotiations in the presence of externalities. We obtain a closed‐form solution for the Markov perfect equilibrium of a multilateral non‐cooperative bargaining model, yielding an equilibrium value and dynamics of negotiations that are supported by experimental studies. Players’ values are monotonically increasing (or decreasing) in the amount of negative (or positive) externalities that they impose on others. Moreover, players’ values are continuous and piecewise linear on the worth of bilateral coalitions, and are inextricably related to their negotiation strategies: the equilibrium value is the Nash bargaining solution when no bilateral coalitions form; the Shapley value when all bilateral coalitions form; or the nucleolus, when either one bilateral coalition among “natural partners” or two bilateral coalitions including a “pivotal player” form.     

Fault tolerance in large games

A Nash equilibrium is an optimal strategy for each player under the assumption that others play according to their respective Nash strategies, but it provides no guarantees in the presence of irrational players or coalitions of colluding players. In fact, no such guarantees exist in general. However, in this paper we show that large games are innately fault tolerant. We quantify the ways in which two subclasses of large games – λ-continuous games and anonymous games – are resilient against Byzantine faults (i.e. irrational behavior), coalitions, and asynchronous play. We also show that general large games have some non-trivial resilience against faults.     

Coalitions, agreements and efficiency

If agents negotiate openly and form coalitions, can they reach efficient agreements? We address this issue within a class of coalition formation games with externalities where agents’ preferences depend solely on the coalition structure they are associated with. We derive Ray and Vohra's [Equilibrium binding agreements, J. Econ. Theory 73 (1997) 30-78] notion of equilibrium binding agreements using von Neumann and Morgenstern [Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944] abstract stable set and then extend it to allow for arbitrary coalitional deviations (as opposed to nested deviations assumed originally). We show that, while the extended notion facilitates the attainment of efficient agreements, inefficient agreements can nevertheless arise, even if utility transfers are possible.     

Partial International Coordination in the Great Fish War

This study extends the great fish war model of Levhari and Mirman [Levhari, D. and Mirman, L. (1980) Bell Journal of Economics 11: 322–344] by incorporating a multiple country context into the model and investigates the existence of a partial coordination Nash equilibrium. First, findings of this paper suggest that a partial coordination scheme is sustainable only in limited cases. Any coalition that has more than two member countries cannot be sustained. Second, the existence and the number of coordinating countries depend critically on the magnitude of the biological and preference parameters. Finally, if the coalition is assumed to be a dominant player, there always exist one or two welfare-improving sustainable coalitions and the size of the sustainable coalitions depends on the parameters of the problem.     

Unobserved heterogeneity and equilibrium: an experimental study of Bayesian and adaptive learning in normal form games

We describe an experiment based on a simple two-person game designed so that different learning models make different predictions. Econometric analysis of the experimental data reveals clear heterogeneity in the subjects’ learning behavior. But the subjects follow only a few decision rules for basing their play on their information, and these rules have simple cognitive interpretations. There is a unique equilibrium in pure strategies, and many equilibria in mixed strategies. We find that the only equilibrium consistent with the data is one of the mixed strategy equilibria. This equilibrium is shown, surprisingly, to be consistent with Jordan's Bayesian model.     

A three-player dynamic majoritarian bargaining game

We analyze an infinitely repeated divide-the-dollar bargaining game with an endogenous reversion point. In each period a new dollar is divided among three legislators according to the proposal of a randomly recognized member—if a majority prefer so—or according to previous period's allocation otherwise. Although current existence theorems for Markovian equilibria do not apply for this dynamic game, we fully characterize a Markov equilibrium. The equilibrium is such that irrespective of the discount factor or the initial division of the dollar, the proposer eventually extracts the whole dollar in all periods. We also show that proposal strategies are weakly continuous in the status quo that equilibrium expected utility is not quasi-concave, and the correspondence of voters’ acceptance set (the set of allocations weakly preferred over the status quo) fails lower hemicontinuity.     

Transplants and Implants: The Economics of Self‐Improvement

This article examines equilibrium self‐improvement and marriage proposal strategies in a two‐sided search model with nontransferable utility. Singles are vertically differentiated—some make better marriage partners than others. A complete characterization of equilibrium is provided. It is shown there are two externalities to self‐improvement decisions. Further, these externalities may support multiple Pareto rankable equilibria. By encouraging everybody to self‐improve, society can create a situation where everybody is forced to improve to remain “acceptable.” But a preferred equilibrium may exist where there is less (costly) self‐improvement.     

A note on Kuhn’s Theorem with ambiguity averse players

Kuhn’s Theorem shows that extensive games with perfect recall can equivalently be analyzed using mixed or behavioral strategies, as long as players are expected utility maximizers. This note constructs an example that illustrates the limits of Kuhn’s Theorem in an environment with ambiguity averse players who use a maxmin decision rule and full Bayesian updating.     

Equilibrium existence in infinite horizon economies

In sequential economies with finite or infinite-lived real assets in positive net supply, we introduce constraints on the amount of borrowing in terms of the market value of physical endowments. We show that, when utility functions are either unbounded and separable in states of nature or separable in commodities, these borrowing constraints not only preclude Ponzi schemes but also induce endogenous Radner bounds on short-sales. Therefore, we obtain existence of equilibrium. Moreover, equilibrium also exists when both assets are numéraire and utility functions are quasilinear in the commodity used as numéraire.     

Bidding for the future: signaling in auctions with an aftermarket

This paper considers auctions where bidders compete for an advantage in future strategic interactions. When bidders wish to exaggerate their private information, equilibrium bidding functions are biased upwards as bidders attempt to signal via the winning bid. Signaling is most prominent in second-price auctions where equilibrium bids are “above value.” In English and first-price auctions, signaling is less extreme since the winner incurs the cost of her signaling choice. The opportunity to signal lowers bidders’ payoffs and raises revenue. When bidders understate their private information, separating equilibria need not exist and the auction may not be efficient.     

On the persistence of corruption

This paper tries to answer the question why the phenomenon of corruption seems to be inherently existent in any society. The dynamic model presented shows how rational agents may generate multiple equilibria of corruption within the same kind of socio-economic system. We assume that the individual disutility caused by the loss of reputation from a corrupt transaction depends on the acceptance of corrupt behavior by the representative individual. Depending on the values of some key parameters like the marginal utility of corrupt behavior and the initial acceptance of corruption a completely corrupt equilibrium where all people completely accept corruption or a completely honest equilibrium where corruption is not accepted at all may be the limit state of the optimal path. Also inner equilibria in-between exist; however, they are always unstable.     

Alliances versus Federations: An Extension of Riker's Analysis of Federal Formation

This essay explores the distinction between federations and alliances and asks the question: When will states choose to federate rather than ally? William Riker argues that a necessary condition for a federal state's formation is that those offering the federal bargain must seek to “expand their territorial control, usually either to meet an external military or diplomatic threat or to prepare for military or diplomatic aggression and aggrandizement.” This argument, though, does not tell us why states sometimes respond to threats by forming federations and at other times by forming alliances. Here we address this issue directly and use a formal model of alliance formation to illustrate our arguments. Briefly, that model assumes states have initial endowments of military and economic resources, where economic resources enter utility functions directly and military capability influences preference only insofar as it determines a state's ability to counter or make threats. State can divert economic resources to military spending, and alliances, in turn, are self-enforcing coalitions designed to augment a state's offensive or defensive capabilities. Federations, which serve the same ends as alliances, are coalitions that need to be enforced by the “higher authority” established when the federation is formed. Our assumption is that states form federations in lieu of alliances if and only if (1) a stable alliance partition does not exist or, if one exists, it is dominated by an unstable partition and (2) if the cost of the loss of sovereignty to each state in the federation is offset by the gains from joining it, relative to what that state secures as its security value.