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.     

Nonmanipulable Bayesian testing

This paper considers the problem of testing an expert who makes probabilistic forecasts about the outcomes of a stochastic process. I show that, as long as uninformed experts do not learn the correct forecasts too quickly, a likelihood test can distinguish informed from uninformed experts with high prior probability. The test rejects informed experts on some data-generating processes; however, the set of such processes is topologically small. These results contrast sharply with many negative results in the literature.     

Learning from private information in noisy repeated games

We study the perfect type-contingently public ex-post equilibrium (PTXE) of repeated games where players observe imperfect public signals of the actions played, and both the payoff functions and the map from actions to signal distributions depend on an unknown state. The PTXE payoffs when players are patient are determined by the solutions to a family of linear programming problems. Using this characterization, we develop conditions under which play can be as if the players have learned the state. We provide a sufficient condition for the folk theorem, and a characterization of the PTXE payoffs in games with a known monitoring structure.     

Belief-free equilibria in games with incomplete information: Characterization and existence

We generalize the results of Hörner and Lovo (2009) [15] to N-player games with arbitrary information structure. First, we characterize the set of belief-free equilibrium payoffs under low discounting as the set of feasible payoffs that are individually rational, jointly rational, and incentive compatible. Second, we provide necessary and sufficient conditions on the information structure for this set to be non-empty.     

Local equilibrium equivalence in probabilistic voting models

Electoral equilibria depend upon candidates' motivations. Maximization of expected vote share may not lead to the same behavior as maximization of the probability of winning the election. Accordingly, it is desirable to understand when electoral equilibria are insensitive to the choice of candidate motivations. This paper examines sufficient conditions for local equilibrium equivalence between expected vote share maximization and maximization of probability of victory in the spatial model of elections with probabilistic voters.     

Hiding an inconvenient truth: Lies and vagueness

When truth conflicts with efficiency, can verbal communication destroy efficiency? Or are lies or vagueness used to hide inconvenient truths? We consider a sequential 2-player public good game in which the leader has private information about the value of the public good. This value can be low, high, or intermediate, the latter case giving rise to a prisoners? dilemma. Without verbal communication, efficiency is achieved, with contributions for high or intermediate values. When verbal communication is added, the leader has an incentive to hide the precise truth when the value is intermediate. We show experimentally that, when communication must be precise, the leader frequently lies, preserving efficiency by exaggerating. When communication can be vague, the leader turns to vague messages when the value is intermediate. Thus, she implicitly reveals all values. Interestingly, efficiency is preserved, since the follower does not seem to realize that vague messages hide inconvenient truths.     

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.     

The value of public information in a Cournot duopoly

We derive alternative sufficient conditions for the value of public information to be either positive or negative in a Cournot duopoly where firms technology exhibits constant returns to scale.     

Error cascades in observational learning: An experiment on the Chinos game

The paper reports an experimental study based on a variant of the popular Chinos game, which is used as a simple but paradigmatic instance of observational learning. There are three players, arranged in sequence,each of which wins a fixed price if she manages to guess the total number of coins lying in everybody?s hands. Our evidence shows that, despite the remarkable frequency of equilibrium outcomes, deviations from optimal play are also significant. And when such deviations occur, we find that, for any given player position, the probability of a mistake is increasing in the probability of a mistake of her predecessors. This is what we call an error cascade, which we measure by evaluating the (heterogeneous) Quantal Response Equilibrium which better suits our data. We also check the robustness of our findings when we allow for belief heterogeneity by applying Kübler and Weizsäcker?s (2004) cognitive frame of limited depth of reasoning.     

Strategic network formation through peering and service agreements

We introduce a game theoretic model of network formation in an effort to understand the complex system of business relationships between various Internet entities (e.g., Autonomous Systems, enterprise networks, residential customers). In our model we are given a network topology of nodes and links where the nodes act as the players of the game, and links represent potential contracts. Nodes wish to satisfy their demands, which earn potential revenues, but may have to pay their neighbors for links incident to them. We incorporate some of the qualities of Internet business relationships, including customer–provider and peering contracts. We show that every Nash equilibrium can be represented by a circulation flow of utility with certain constraints. This allows us to prove bounds on the prices of anarchy and stability. We also focus on the quality of equilibria achievable through centralized incentives.     

Axioms for minimax regret choice correspondences

This paper unifies and extends the recent axiomatic literature on minimax regret. It compares several models of minimax regret, shows how to characterize the according choice correspondences in a unified setting, extends one of them to choice from convex (through randomization) sets, and connects them by defining a behavioral notion of perceived ambiguity. Substantively, a main idea is to behaviorally identify ambiguity with failures of independence of irrelevant alternatives. Regarding proof technique, the core contribution is to uncover a dualism between choice correspondences and preferences in an environment where this dualism is not obvious. This insight can be used to generate results by importing findings from the existing literature on preference orderings.     

Rents, military elites, and political democracy

In autocratic regimes the military elite is in a position to extract rents, because without the support of the military the government is in general not able to sustain itself. In this paper, we empirically confirm the negative relation between transfers to the military and the degree of democracy for developing countries. We use an instrumental variable approach to account for the simultaneity that arises since the degree of democracy is itself a function of transfers to the military.     

Non-cooperative solutions for estate division problems

In an estate division problem an estate has to be divided among several players whose total entitlement to the estate exceeds its size. This paper extends the non-cooperative approach through a claim game, as initiated by O?Neill (1982), by allowing players to put multiple claims on the same part of the estate, and by considering the case where individual entitlements may exceed the estate. A full characterization of the set of Nash equilibria of the claim game is obtained both for restricted estate division problems, where individual entitlements do not exceed the estate, and for the general case. Variations on the claim game are considered, which result in proportional division in equilibrium.     

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.     

Stationary monetary equilibria with strictly increasing value functions and non-discrete money holdings distributions: An indeterminacy result

In this paper, we present a search model with divisible money in which there exists a continuum of monetary equilibria with strictly increasing continuous value functions and with non-discrete money holdings distributions.     

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.     

Pre-sale information

In markets as diverse as that for specialized industrial equipment or that for retail financial services, sellers or intermediaries may earn profits both from the sale of products and from the provision of pre-sale consultation services. We study how a seller optimally chooses the costly quality of pre-sale information, next to the price of information and the product price, and obtain clear-cut predictions on when information is over- and when it is underprovided, even though we find that information quality does not satisfy a standard single-crossing property. Buyers who are a priori more optimistic about their valuation end up paying a higher margin for information but a lower margin for the product when they subsequently exercise their option to purchase at a pre-specified price.