A General Solution to King Solomon's Dilemma

In general terms, Solomon's dilemma is this. There are many agents. An object must be awarded at no cost to the one agent who values it most. We provide a mechanism that implements this outcome in iteratively weakly undominated strategies when it is common knowledge that the agent who most values the object knows who he is.Journal of Economic LiteratureClassification Numbers: C60, C72, D61, D74, D82.     

Asymmetric information about rivals'' types in standard auctions

We study auctions in which bidders may know the types of some rival bidders but not others. This asymmetry in bidders' knowledge about rivals' types has different effects on the two standard auction formats. In a second-price auction, it is weakly dominant to bid one's valuation, so the knowledge of rivals' types has no effect, and the good is allocated efficiently. In a first-price auction, bidders refine their bidding strategies based on their knowledge of rivals' types, which yields an inefficient allocation. We show that the inefficient allocation in the first-price auction translates into a poor revenue performance. Given a standard regularity condition, the seller earns higher expected revenue from the second-price auction than from the first-price auction, whereas the bidders are better off from the latter.     

Incentives in the probabilistic serial mechanism

The probabilistic serial mechanism (Bogomolnaia and Moulin, 2001 [9]) is ordinally efficient but not strategy-proof. We study incentives in the probabilistic serial mechanism for large assignment problems. We establish that for a fixed set of object types and an agent with a given expected utility function, if there are sufficiently many copies of each object type, then reporting ordinal preferences truthfully is a weakly dominant strategy for the agent (regardless of the number of other agents and their preferences). The non-manipulability and the ordinal efficiency of the probabilistic serial mechanism support its implementation instead of random serial dictatorship in large assignment problems.     

Network architecture, salience and coordination

This paper reports the results of an experimental investigation of dynamic games in networks. In each period, the subjects simultaneously choose whether or not to make an irreversible contribution to the provision of an indivisible public good. Subjects observe the past actions of other subjects if and only if they are connected by the network. Networks may be incomplete so subjects are asymmetrically informed about the actions of other subjects in the same network, which is typically an obstacle to the attainment of an efficient outcome. For all networks, the game has a large set of (possibly inefficient) equilibrium outcomes. Nonetheless, the network architecture makes certain strategies salient and this in turn facilitates coordination on efficient outcomes. In particular, asymmetries in the network architecture encourage two salient behaviors, strategic delay and strategic commitment. By contrast, we find that symmetries in the network architecture can lead to mis-coordination and inefficient outcomes.     

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.     

Local coordination and market equilibria

We reformulate the local stability analysis of market equilibria in a competitive market as a local coordination problem in a market game, where the map associating market prices to best-responses of all traders is common knowledge and well-defined both in and out of equilibrium. Initial expectations over market variables differ from their equilibrium values and are not common knowledge. This results in a coordination problem as traders use the structure of the market game to converge back to equilibrium. We analyse a simultaneous move and a sequential move version of the market game and explore the link with local rationalizability.     

ROBUST RATIONALIZABILITY UNDER ALMOST COMMON CERTAINTY OF PAYOFFS

An action is robustly rationalizable if it is rationalizable for every type who has almost common certainty of payoffs. We illustrate by means of an example that an action may not be robustly rationalizable even if it is weakly dominant, and argue that robust rationalizability is a very stringent refinement of rationalizability. Nonetheless, we show that every strictly rationalizable action is robustly rationalizable. We also investigate how permissive robust rationalizability becomes if we require that players be fully certain of their own payoffs.     

THE SECOND‐PRICE AUCTION SOLVES KING SOLOMON'S DILEMMA*

The planner wants to give k identical, indivisible objects to the top k valuation agents at zero costs. Each agent knows her own valuation of the object and whether it is among the top k. Modify the (k+ 1)st‐price sealed‐bid auction by introducing a small participation fee and the option not to participate in it. This simple mechanism implements the desired outcome in iteratively undominated strategies. Moreover, no pair of agents can profitably deviate from the equilibrium by coordinating their strategies or bribing each other.     

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.     

Evolutionary selection of ‘chivalrous’ conventions in coordination games without common expectations

We study an evolutionary game-theoretic model where players have to choose within a predetermined set of mixed strategies in a coordination game. Players are of two different kinds, male and female. No common expectations assumption is made; players tend therefore to adopt the strategy that yields larger than average expected payoffs for their kind. In this framework, every stable stationary point of the population dynamics can be interpreted as the emergence of a particular convention. A classification of the possible conventions is provided; conditions for their emergence are determined.     

Behavioral spillovers and cognitive load in multiple games: An experimental study

We present evidence from laboratory experiments of behavioral spillovers and cognitive load that spread across strategic contexts. In the experiments, subjects play two distinct games simultaneously with different opponents. We find that the strategies chosen and the efficiency of outcomes in one game depends on the other game that the subject plays, and that play is altered in predictable directions. We develop a measure of behavioral variation in a normal form game, outcome entropy, and find that prevalent strategies in games with low outcome entropy are more likely to be used in the games with high outcome entropy, but not vice versa. Taken together, these findings suggest that people do not treat strategic situations in isolation, but may instead develop heuristics that they apply across games.     

A Blotto game with multi-dimensional incomplete information

We examine a multi-dimensional incomplete information Colonel Blotto game in which each player’s n-tuple of battlefield valuations is drawn from a common n-variate joint distribution function that is uniform on the non-negative orthant of the surface of a sphere.     

Admissibility and common belief

The concept of ‘fully permissible sets’ is defined by an algorithm that eliminates strategy subsets. It is characterized as choice sets when there is common certain belief of the event that each player prefer one strategy to another if and only if the former weakly dominates the latter on the set of all opponent strategies or on the union of the choice sets that are deemed possible for the opponent. The concept refines the Dekel–Fudenberg procedure and captures aspects of forward induction.     

Comment on “Correlated information, mechanism design and informational rents” [J. Econ. Theory 123 (2) (2005) 210–217]

We amend an error in [S. Parreiras, Correlated information, mechanism design and informational rents, J. Econ. Theory 123 (2005) 210–217]. Consequently, it is in general not possible to reinterpret a mechanism design model that violates the spanning condition of Crémer and McLean [J. Crémer, R. McLean, Full extraction of the surplus in bayesian, dominant strategy auctions, Econometrica 56 (1988) 1247–1258] as one in which agents hold private information about the informativeness of their signals about other agents? types. Instead, such an interpretation is warranted only when the weights used to span an agent?s set of beliefs stand in a singular relation with the prior type distribution that is known as an alternative characterization of Blackwell dominance.     

Advice and behavior in intergenerational ultimatum games: An experimental approach

In the real world, when people play a game, they often receive advice from those that have played it before them. Such advice can facilitate the creation of a convention of behavior. This paper studies the impact of advice on the behavior subjects who engage in a non-overlapping generational Ultimatum game where after a subject plays he is replaced by another subject to whom he can offer advice.Our results document the fact that allowing advice fosters the creation of a convention of behavior in Ultimatum games. In addition, by reading the advice offered we conclude that arguments of fairness are rarely used to justify the offers of Senders but are relied upon to justify rejections by Receivers.     

Sequential auctions with randomly arriving buyers

We analyze a dynamic market in which buyers compete in a sequence of private-value auctions for differentiated goods. New buyers and new objects may arrive at random times. Since objects are imperfect substitutes, buyers? values are not persistent. Instead, each buyer?s private value for a new object is a new independent draw from the same distribution.We consider the use of second-price auctions for selling these objects, and show that there exists a unique symmetric Markov equilibrium in this market. In equilibrium, buyers shade their bids down by their continuation value, which is the (endogenous) option value of participating in future auctions. We characterize this option value and show that it depends not only on the number of buyers currently present on the market and the distribution of their values, but also on anticipated market dynamics.     

Bargaining under a deadline: evidence from the reverse ultimatum game

We study a “reverse” ultimatum game, in which proposers have multiple chances to offer responders a division of some fixed pie. The game ends if the responder accepts an offer, or if, following a rejection, the proposer decides not to make a better offer. The unique subgame perfect equilibrium gives the proposer the minimum possible payoff. Nevertheless, the experimental results are not too different from those of the standard ultimatum game, although proposers generally receive slightly less than half of the surplus.We use the reverse ultimatum game to study deadlines experimentally. With a deadline, the subgame perfect equilibrium prediction is that the proposer gets the entire surplus.Deadlines are used strategically to influence the outcome, and agreements are reached near the deadline. Strategic considerations are evident in the differences in observed behavior between the deadline and no deadline conditions, even though agreements are substantially less extreme than predicted by perfect equilibrium.     

Kernel-based type spaces

Type space is of fundamental importance in epistemic game theory. This paper shows how to build type space if players approach the game in a way advocated by Bernheim's justification procedure. If an agent fixes a strategy profile of her opponents and ponders which of their beliefs about her set of strategies make this profile optimal, such an analysis is represented by kernels and yields disintegrable beliefs. Our construction requires that underlying space is Polish.     

UNIQUENESS OF EQUILIBRIUM PAYOFFS IN FINITELY REPEATED GAMES WITH IMPERFECT MONITORING*

This paper examines when a finitely repeated game with imperfect monitoring has a unique equilibrium payoff vector. This problem is nontrivial under imperfect monitoring, because uniqueness of equilibrium (outcome) in the stage game does not extend to finitely repeated games. A (correlated) equilibrium is equilibrium minimaxing if any player's equilibrium payoff is her minimax value when the other players choose a correlated action profile from the actions played in the equilibrium. The uniqueness result holds if all stage game correlated equilibria are equilibrium minimaxing and have the same payoffs. The uniqueness result does not hold under weaker conditions.