Signaling in a Rent‐Seeking Contest with One‐Sided Asymmetric Information

We consider a two‐player rent‐seeking Tullock contest where one player has private information about his valuation of the prize, which can be high or low. This player can send a costly signal to his opponent, i.e., he can commit to reduce the prize either by some absolute amount of money or proportionally, conditional on winning it. We show that both kinds of signaling imply completely opposite results for separating equilibria, both in terms of conditions for existence and the type of player who sends the costly signal.     

Coordination between a sophisticated and fictitious player

Successful coordination is a common and important social problem. Achieving it relies on the players’ ability to accurately anticipate future choices from known information. Individuals may not only lack this cognitive ability, but differ in it. Fictitious Play is an adaptive behavior where a myopic best response to the historical play of an opponent is selected. I consider the interaction between a fictitious player and a sophisticated player in 2 × 2 coordination games. The existence of coordination, the selection of equilibria, and the payoffs generated are analyzed.     

On the convergence to the Nash bargaining solution for action-dependent bargaining protocols

We consider a non-cooperative multilateral bargaining game and study an action-dependent bargaining protocol, that is, the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected. An important example is the frequently studied rejector-becomes-proposer protocol. We focus on subgame perfect equilibria in stationary strategies which are shown to exist and to be efficient. Equilibrium proposals do not depend on the probability to propose conditional on the rejection by another player. We consider the limit, as the bargaining friction vanishes. In case no player has a positive probability to propose conditional on his rejection, each player receives his utopia payoff conditional on being recognized. Otherwise, equilibrium proposals of all players converge to a weighted Nash bargaining solution, where the weights are determined by the probability to propose conditional on one's own rejection.     

Bargaining and efficiency in networks

We study an infinite horizon game in which pairs of players connected in a network are randomly matched to bargain over a unit surplus. Players who reach agreement are removed from the network without replacement. The global logic of efficient matchings and the local nature of bargaining, in combination with the irreversible exit of player pairs following agreements, create severe hurdles to the attainment of efficiency in equilibrium. For many networks all Markov perfect equilibria of the bargaining game are inefficient, even as players become patient. We investigate how incentives need to be structured in order to achieve efficiency via subgame perfect, but non-Markovian, equilibria. The analysis extends to an alternative model in which individual players are selected according to some probability distribution, and a chosen player can select a neighbor with whom to bargain.     

Learning from Personal Experience: One Rational Guy and the Justification of Myopia

The paper examines a large population analog of fictitious play in which players learn from personal experience, focusing on what happens when a single rational player is added to the population. Because the learning process naturally generates contagion dynamics, the rational player at times has an incentive to act nonmyopically. In 2 × 2 games the dynamics are asymmetric and favor risk dominant equilibria. A variety of other examples are presented.Journal of Economic LiteratureClassification Number: C7.     

A two-person game of information transmission

We consider a statistical decision problem faced by a two player organization whose members may not agree on outcome evaluations and prior probabilities. One player is specialized in gathering information and transmitting it to the other, who takes the decision. This process is modeled as a game. Qualitative properties of the equilibria are analyzed. The impact of improving the quality of available information on the equilibrium welfares of the two individuals is studied. Better information generally may not improve welfare. We give conditions under which it will.     

Game theory and speculation on government bonds

The aim of this paper is to propose a method to stabilize the rapid variations on the value of government bonds issued by the States, using Game Theory. In particular, we focus our attention on three players: a large speculative bank (hereinafter called Speculator), having immediate access to the market of government bonds, the European Central Bank (ECB) and a State in economic crisis, with a high public debt. In this regard, we will analyze the interaction between these three subjects: the Speculator, our first player, the ECB, our second player, and the State, our third player. The financial crisis, that hit the market of European government bonds, showed us that large speculators can influence the financial markets and benefit from the creation of arbitrage opportunities caused by themselves. In this way, the default probability of States in economic difficulty increases significantly and alarmingly. We already heard to talk about concepts like “spread” and “public debt,” which has crippled the economies of great States, for instance Italy. In this paper we propose on financial transactions the introduction of a tax, which hits only the speculative profits. We show how the above tax would probably be able to avert the speculation. For this purpose, we compare the different behaviors adopted by the Speculator and by the ECB in case of absence or presence of the tax, with the consequent effects on the State that sells its government bonds, paying particular attention to the movement of the game equilibria. In fact, with the introduction of our tax, all equilibria of the game become excellent for the State in economic difficulty.     

Commitment Robust Equilibria and Endogenous Timing

This paper investigates which equilibria of a game are still viable when players have the opportunity to commit themselves. To that end we study a model of endogenous timing in which players face the trade-off between committing early and moving late. It is shown that mixed (resp. pure) equilibria of the original game are subgame perfect (resp. persistent) in the timing game only when no player has an incentive to move first. Consequently, mixed equilibria are viable only if no player has an incentive to move first. One needs strong evolutionary solution concepts to draw that conclusion for pure equilibria.Journal of Economic LiteratureClassification Number: C72.     

Congestion games with malicious players

We study the equilibria of non-atomic congestion games in which there are two types of players: rational players, who seek to minimize their own delay, and malicious players, who seek to maximize the average delay experienced by the rational players. We study the existence of pure and mixed Nash equilibria for these games, and we seek to quantify the impact of the malicious players on the equilibrium. One counterintuitive phenomenon which we demonstrate is the “windfall of malice”: paradoxically, when a myopically malicious player gains control of a fraction of the flow, the new equilibrium may be more favorable for the remaining rational players than the previous equilibrium.     

Repeated signaling games

I analyze a class of repeated signaling games in which the informed player's type is persistent and the history of actions is perfectly observable. In this context, a large class of possibly complex sequences of signals can be supported as the separating equilibrium actions of the “strong type” of the informed player. I characterize the set of such sequences. I also characterize the sequences of signals in least cost separating equilibria (LCSE) of these games. In doing this, I introduce a state variable that can be interpreted as a measure of reputation. This gives the optimization problem characterizing the LCSE a recursive structure. I show that, in general, the equilibrium path sequences of signals have a simple structure. The shapes of the optimal sequences depend critically on the relative concavities of the payoff functions of different types, which measure the relative preferences towards payoff smoothing.     

A One-Stage Model of Link Formation and Payoff Division

In this paper we introduce a strategic form model in which cooperation structures and divisions of the payoffs are determined simultaneously. We analyze the cooperation structures and payoff divisions that result according to Nash equilibria, strong Nash equilibria, and coalition proof Nash equilibria. We find that no cycle will be formed if a player claims a positive amount for the formation of one of its links and that a player does not necessarily profit from a central position in a cooperation structure. Journal of Economic Literature Classification Numbers: C71, C72.     

UNEMPLOYMENT, HYSTERESIS AND TRANSITION

In this paper, we quantify the degree of persistence in the unemployment rates of transition countries using a variety of methods benchmarked against the EU. Initially, we work with the concept of linear ‘Hysteresis’ as described by the presence of unit roots in unemployment as in most empirical research on this area. Given that this is potentially a narrow definition, we also take into account the existence of structural breaks and nonlinear dynamics in unemployment. Finally, we examine whether CEECs' unemployment presents features of multiple equilibria, that is, if it remains locked into a new level whenever some structural change or sufficiently large shock occurs. Our findings show that, in general, we can reject the unit‐root hypothesis after controlling for structural changes and business‐cycle effects, but we can observe the presence of a high and low unemployment equilibria. The speed of adjustment is faster for CEECs than the EU, although CEECs tend to move more frequently between equilibria.     

Markov perfect equilibria in industries with complementarities

Summary.   This paper considers the existence and computation of Markov perfect equilibria in games with a “monotone” structure. Specifically, it provides a constructive proof of the existence of Markov perfect equilibria for a class of games in which a) there is a continuum of players, b) each player has the same per period payoff function and c) these per period payoff functions are supermodular in the player's current and past action and have increasing differences in the player's current action and the entire distribution of actions chosen by other players. The Markov perfect equilibria that are analyzed are symmetric, not in the sense that each player adopts the same action in any period, but rather in the sense that each player uses the same policy function. Since agents are typically distributed across many states they will typically take different actions. The formal environment considered has particular application to models of industries (or economies) in which firms face costs of price adjustment. It is in this context that the results are developed. Received: November 9, 1999; revised version: February 10, 2000     

The lifeboat problem

We study an all-pay contest with multiple identical prizes (“lifeboat seats”). Prizes are partitioned into subsets of prizes (“lifeboats”). Players play a two-stage game. First, each player chooses an element of the partition (“a lifeboat”). Then each player competes for a prize in the subset chosen (“a seat”). We characterize and compare the subgame perfect equilibria in which all players employ pure strategies or all players play identical mixed strategies in the first stage. The partitioning of prizes can lead to coordination failure when players employ nondegenerate mixed strategies. In these equilibria some rents are sheltered and rent dissipation is reduced.     

On Sustaining Cooperation without Public Observations

This paper examines a dynamic game in which each player only observes a private and imperfect signal on the actions played. Our main result is that in a repeated prisoner's dilemma where defections are irreversible (at least for a long enough period of time), patient enough players may achieve almost efficient outcomes. Dealing with models of imperfect private monitoring is difficult because (i) continuation games are games of incomplete information, hence they do not have the same structure as the original game. In particular, continuation equilibria are correlated equilibria. (ii) Players are typically uncertain about their opponents' past observations and actions, and they use their entire own private history to learn about these actions. As a result equilibrium strategies are in general nontrivial and increasingly complex functions of past observations. We bypass these difficulties by looking at correlated equilibria of the original game and find correlated equilibria in which the decision problem faced by each player remains the same over time. Journal of Economic Literature Classification Numbers: C72.     

Buying Influence: Aid Fungibility in a Strategic Perspective

I study equilibria of non‐cooperative games between an aid donor and a recipient when there is conflict over the allocation of their combined budgets. The general conclusion is that a donor's influence over outcomes is increasing in the share of the available resources it controls; if this share is large enough, aid fungibility is not important as the donor achieves its most preferred allocation. The game‐theoretic approach to fungibility is contrasted with the traditional non‐strategic approach. I argue that the former is superior as it derives final allocations instead of assuming them, making analysis of the sources of influence over outcomes possible.     

Are sequential round‐robin tournaments discriminatory?

I examine sequential round‐robin tournaments with three and four symmetric players. Each player is matched once with each other player and each match is organized as a Tullock contest. A single prize is allocated to the player with the most matches won. I show that, depending on the position of their matches in the sequence of the tournament, the players' ex ante winning probabilities and expected payoffs differ. Compared to tournaments with matches organized as all‐pay auctions, however, discrimination is weaker and partially reversed. Moreover, aggregate effort in tournaments with suitable Tullock contests is larger than in tournaments with all‐pay auctions. The fairness of round‐robin tournaments may be improved by an endogenous sequence of matches or the requirement that players fix their effort ex ante.     

Infinite Histories and Steady Orbits in Repeated Games

We study a model of repeated games with the following features: (a) Infinite histories. The game has been played since days of yore, or is so perceived by the players: (b) Turing machines with memory. Since regular Turing machines coincide with bounded recall strategies (in the presence of infinite histories), we endow them with "external" memory; (c) Nonstrategic players. The players ignore complicated strategic considerations and speculations about them. Instead, each player uses his/her machine to update some statistics regarding the others′ behaviour, and chooses a best response to observed behaviour. Relying on these assumptions, we define a solution concept for the one shot game, called steady orbit. The (closure of the) set of steady orbit payoffs strictly includes the convex hull of the Nash equilibria payoffs and is strictly included in the correlated equilibria payoffs. Assumptions (a)–(c) above are independent to a large extent. In particular, one may define steady orbits without explicitly dealing with histories or machines.     

Contests with limited resources

Many interesting phenomena (electoral competition, R&D races, lobbying) are instances of multiple simultaneous contests with unconditional commitment of limited resources. Specifically, the following game is analyzed. Two players compete in a number of simultaneous contests. The players have limited resources (budgets) and must decide how to allocate these to the different contests. In each contest the player who expends more resources than his adversary wins a corresponding prize. Mixed-strategy equilibria are characterized in the case of identical values and budgets and the connections with the classical Blotto game are analyzed.     

Variable temptations and black mark reputations

Reputations often guide sequential decisions to trust and to reward trust. We consider situations where each player is randomly matched with a partner in every period. One player – the truster – decides whether to trust. If trusted, the other player – the temptee – has a temptation to betray. The strength of temptation, private information to the temptee, varies across encounters. Betrayals are recorded as publicly known black marks. First, we identify equilibria when players only condition on the number of a temptee's black marks. Second, we show that conditioning on the number of interactions as well as on the number of black marks does not prolong trust. Third, we examine stochastic variations where black marks may be forgotten. Perhaps surprisingly, such variations do not improve outcomes. Fourth, when players condition on more general summary statistics of a temptee's past, we study equilibria where trust is suspended temporarily.