The B.E. Journal of Theoretical Economics

On Rationalizability and Beliefs in Discrete Private-Value First-Price Auctions

Jack Robles et al. — Fri, 11 May 2012 11:19:14 PDT

We extend Dekel and Wolinsky's (2003) result on private-value first price auctions by providing different sufficient conditions under which each player has a unique rationalizable bid conditional on her value. Unlike Dekel and Wolinsky's, our result does not necessarily require a large number of players. If values are independently distributed, (i) our conditions are weaker than Dekel and Wolinsky's, and (ii) our conditions require a large number of players only if the distributions on values has a low reverse hazard rate for some value. Our result holds for the cases where players' utility functions are concave or values are not identically distributed.

Screening and Financial Contracting in the Face of Outside Competition

Dan Bernhardt — Fri, 11 May 2012 11:19:07 PDT

This paper considers an investor who, at a cost, can acquire a signal about an entrepreneurial project's payoff. The problem for this investor is that uninformed investors can compete to provide funding and the informed investor's contract offer conveys information to the entrepreneur about the project's likely payoffs, affecting the attractiveness of the entrepreneur's uninformed funding alternatives. I determine how the investor's choices of signal quality and contracting terms are affected by project primitives. I prove that equilibrium expected payoffs in this signaling game are unique and that equilibrium strategies solve simple optimal contracting problems, showing that informed investors can use equity, and that uninformed investors compete with simple debt. Finally, I show that introducing the possibility of commitment by the informed investor alters the structure of the game, but not equilibrium payoffs.

Correlation in the Multiplayer Electronic Mail Game

Peter A. Coles et al. — Fri, 04 May 2012 22:20:55 PDT

In variants of the Electronic Mail Game (Rubinstein, 1989) where two or more players communicate via multiple channels, the multiple channels can facilitate collective action via redundancy, the sending of the same message along multiple paths or else repeatedly along the same path (Chwe, 1995 and De Jaegher, 2011). This paper offers another explanation for how multiple channels may permit collective action: parties may be able to coordinate their actions when messages’ arrivals at their destinations are sufficiently correlated events. Correlation serves to fill in information gaps that arise when players are uncertain of the source of message failure, effectively strengthening messages from one player. This asymmetry in message strength in turn permits cutoff equilibria, where players take action after receiving a minimum number of confirmations.

Multidimensional Product Differentiation with Discrete Characteristics

Mariano G. Runco — Mon, 23 Apr 2012 20:59:36 PDT

In this paper we consider a duopoly model of multidimensional vertical product differentiation where product features are discrete and consumers' tastes are described by a joint density function that belongs to the class of Elliptically Contoured Distributions. We prove that in any equilibrium one firm always includes all characteristics in the product. Moreover, when types have perfect positive correlation the unique equilibrium involves maximum differentiation. More importantly, the main result states that the other firm's equilibrium level of differentiation is determined by the correlation among types.

Characterizing Welfare-egalitarian Mechanisms with Solidarity When Valuations are Private Information

Duygu Yengin — Mon, 23 Apr 2012 01:07:20 PDT

In the problem of assigning indivisible goods and monetary transfers, we characterize welfare-egalitarian mechanisms (that are decision-efficient and incentive compatible) with an axiom of solidarity under preference changes and a fair ranking axiom of order preservation. This result is in line with characterizations of egalitarian rules with solidarity in other economic models. We also show that we can replace order-preservation with egalitarian-equivalence or no-envy (on the subadditive domain) and still characterize the welfare-egalitarian class. However, if we weaken order preservation to symmetry, mechanisms that are not welfare-egalitarian exist. We also study upper bounds on deficit and welfare lower bounds that characterize subclasses of the welfare-egalitarian class.

A Folk Theorem for Games when Frequent Monitoring Decreases Noise

António M. Osório — Mon, 23 Apr 2012 01:07:19 PDT

This paper studies frequent monitoring in an infinitely repeated game with imperfect public information and discounting, where players observe the state of a continuous time Brownian process at moments in time of length Δ. It shows that a limit folk theorem can be achieved with imperfect public monitoring when players monitor each other at the highest frequency, i.e., Δ↓0. The approach assumes that the expected joint output depends exclusively on the action profile simultaneously and privately decided by the players at the beginning of each period of the game, but not on Δ. The strong decreasing effect on the expected immediate gains from deviation when the interval between actions shrinks, and the associated increase precision of the public signals, make the result possible in the limit.

The Tennis Coach Problem: A Game-Theoretic and Experimental Study

Ayala Arad — Mon, 23 Apr 2012 01:07:16 PDT

The paper introduces a new allocation game, related to Blotto games: each tennis coach assigns his four different skilled players to four positions, and then each team plays all other teams in the tournament. The winning team is the one with the highest total score.

The set of equilibria is characterized and experimental behavior in variants of the game is analyzed in light of an adapted level-k model which is based on an appealing specification of the starting point (Level-0). The results exhibit a systematic pattern- a majority of the subjects used a small number of strategies. However, although level-k thinking is naturally specified in this context, only a limited use of (low) level-k thinking was found. These findings differ from those obtained in previous studies, which found high frequencies of level-k reasoning among subjects in various games. Thus, the results illuminate some bounds of the level-k approach.

Strict Concavity of the Value Function for a Family of Dynamic Accumulation Models

Eugenio S.A. Bobenrieth et al. — Fri, 20 Apr 2012 06:46:47 PDT

We prove strict concavity of the value function for liquidity constrained dynamic accumulation models without adopting at least one of the following restrictive assumptions: zero response of productive effort, bounded marginal value of accumulated balances, or strictly convex cost of holding accumulated balances. Thus we extend well known theoretical results to more general models of saving with liquidity constraints and of commodity storage with non-negativity constraints on stocks. Our results provide a foundation for estimation of a homogeneous markovian process for consumption in models of saving, or for price in commodity storage models, under more realistic assumptions.

Seller Cheap Talk in Almost Common Value Auction

Daniel Zhiyun LI — Fri, 16 Mar 2012 06:38:42 PDT

We study seller cheap talk problem in a modified almost common value auction, where there are potential entrants who need to pay entry costs for entering the auction. In almost common value auctions, a seller suffers great revenue losses due to the aggravated winner's curse problem. In our modified model, the inside bidders are more sensitive to the signals sent by the seller, and by revealing the information about the object valuation, the seller faces the trade-off between the benefit of increased competition and that of higher bids by weak inside bidders. For instance, a low message will attract the potential entrants into the auction, as a result of greater winning opportunity, and a high message will encourage the weak since bidders to bid more aggressively, as a result of increased valuation. Under quite plausible conditions, there exists an informative equilibrium in this cheap talk game, which will either increase the expected revenue of the auction, or the efficiency of final allocation.

Two Notes on the Blotto Game

Jonathan Weinstein — Thu, 15 Mar 2012 02:43:40 PDT

We exhibit a new equilibrium of the classic Blotto game in which players allocate one unit of resources among three coordinates and try to defeat their opponent in two out of three. It is well known that a mixed strategy will be an equilibrium strategy if the marginal distribution on each coordinate is U[0,(2/3)]. All classic examples of such distributions have two-dimensional support. Here we exhibit a distribution which has one-dimensional support and is simpler to describe than previous examples. The construction generalizes to give one-dimensional distributions with the same property in higher-dimensional simplices as well.

As our second note, we give some results on the equilibrium payoffs when the game is modified so that players have unequal budgets. Our results suggest a criterion for equilibrium selection in the original symmetric game, in terms of robustness with respect to a small asymmetry in resources.

Career Concerns and Performance Reporting in Optimal Incentive Contracts

Alexander Wolitzky — Tue, 21 Feb 2012 05:24:34 PST

In many contracting settings incentives are provided not only through transfers but also through performance reports to prospective employers. This paper studies a principal-agent model of this kind, in which the principal sends a non-verifiable report of output to a competitive labor market interested in the agent's ability. It is assumed that the principal and agent write an enforceable contract over both payments and reports as a function of output, and that the contract terms they agree to cannot be observed by the market. When contracts are unrestricted, reports cannot affect the agent's future wage in equilibrium, because the agent will always pay the principal to give a good report. Under limited liability, reports can affect future wages, but only by designating output as "good" or "bad." This informative performance reporting benefits the principal, and may more than make up for the costs imposed by limited liability. The possibilities that the market may have some direct information about output, that the principal may have additional information about the agent's ability, and that the principal may have psychological or reputational costs of misreporting output are also considered.

Information Theory and Observational Limitations in Decision Making

David Wolpert et al. — Tue, 24 Jan 2012 20:45:42 PST

We introduce a general framework for formalizing and analyzing the problem faced by a Decision Maker (DM) working under information-theoretic constraints on their observational ability. The random utility model and the "hedonic utility" model of Netzer and Robson (NR) are special cases of this framework. We begin by applying information theory to our framework to derive general results concerning the expected regret of DM under observational limitations. We then turn our attention to the effects of observational limitations on choice behavior (rather than their effects on the regret values induced by that behavior). We focus on the special case of NR. First we derive two postulates assumed by NR. We then provide a simple derivation of the result of NR that a particular hedonic utility function satisfies certain optimality principles. Next we extend NR to allow a countable, rather than uncountable, set of states of the world. In particular we show how to use dynamic programming to solve for the optimal preference order of DM in this extension. We also extend NR by considering the case where more than two options are presented to DM. In particular, we show that the results of NR change in such a case, implying that the number of options being presented is a crucial aspect of choice problems.

Transparency, Career Concerns, and Incentives for Acquiring Expertise

Heski Bar-Isaac — Tue, 24 Jan 2012 20:45:38 PST

An agent, who cares about signaling his ability, chooses among different projects that generate observable outcomes. The agent's information about which project delivers a good outcome depends on both his ability and his effort. This paper examines how the agent's incentives for effort change depending on whether or not the agent's project choice is observed. If this choice is publicly observed, the agent's project choice is distorted towards particular types of projects. When the outcomes of these advantaged projects are particularly sensitive to the agent's information, such transparency boosts the agent's information-gathering incentives. However, when public observation of project choice leads the agent to choose information-insensitive projects, then such transparency dampens incentives. This provides a more nuanced view of the implications of action transparency in the literature on career concerns for experts.

Preference for Variety

Karen Kaiser et al. — Tue, 10 Jan 2012 21:28:52 PST

We consider a decision maker who enjoys choosing from a varied set of alternatives. Building on behavioral evidence, we propose testable axioms which characterize preference for variety and provide a representation theorem. We go on to illustrate the potential effects of preference for variety in a model of retailing. Consumer welfare may be decreasing in the competitiveness of the retailing sector as competition eliminates the scope for retailers to offer variety. Mainstream consumers with a preference for variety and consumers with eccentric tastes enjoy a symbiotic relationship. Competition over mainstream consumers makes retailers offer more exotic goods, while eccentric consumers subsidize their carrying costs.

An Experimental Comparison of Sequential First- and Second-Price Auctions with Synergies

Kasper Leufkens et al. — Wed, 04 Jan 2012 00:23:13 PST

Using laboratory experiments, we compare the performance of first-price and second-price auctions when two stochastically equivalent objects are auctioned sequentially and the winner of the first auction receives a positive synergy in the second auction. According to the risk-neutral subgame perfect Nash equilibrium, the second-price auction provides more efficiency and a higher revenue to the seller, but a lower ex ante expected payoff to the bidders. Our experimental data indicate precisely the opposite results for format comparisons: the first-price auction gives rise to larger levels of efficiency and revenue, but lower payoffs to the bidders. Despite the lower payoff, the likelihood of an ex post loss is also smaller under the first-price auction. Our results therefore support the common use of the first-price auction in governmental and business-to-business procurements.

Uniquely Representing “A Preference for Uniformity”

Kalyan Chatterjee et al. — Tue, 03 Jan 2012 20:02:04 PST

In a model of decision making over sets of alternatives, we consider an agent who conceives of the different utilities she will receive (depending on the state of mind she is in, her subjective state) when she finally makes a choice from the set. Her uncertainty is described by multiple beliefs (or measures) over the state space. She is pessimistic about the true beliefs, and would like to hedge her bets. This results in her having a preference for uniformity of payoffs across the various subjective states. We present a utility representation for such agents and show that our representation provides a natural measure of the agent's desire for uniformity of payoffs in the subjective states. We also show that concerns for uniformity are orthogonal to concerns about flexibility or commitment. We achieve this by relaxing the Independence axiom as applied to our environment. However, this weakening of Independence means that in settings with temptation, we can no longer ensure the existence of a unique normative ranking.

Sellers Like Clusters

Klaus Kultti — Mon, 12 Dec 2011 20:31:10 PST

I study an economy with sellers and buyers. The sellers are capacity constrained and face stochastic demand. They may locate close to each other, cluster, or separately. In the former case the buyers can visit any of them, while in the latter case the buyers can visit only one of them. The sellers post prices which are observed by the buyers who base their decision to contact sellers on the prices. I explicitly derive the equilibrium prices or price strategies in the clustered and in the non-clustered market for an arbitrary distribution of demand. I show that the clustered market often yields higher profits than the non-clustered. Finally, I allow the sellers to choose both the market and prices, and show that the equilibrium market structure features clustering.

Make-or-Buy Decisions and the Manipulability of Performance Measures

Fredrik Andersson — Thu, 01 Dec 2011 03:03:52 PST

The make-or-buy decision is analyzed in a simple framework combining contractual incompleteness with the existence of an imperfect but contractible performance measure. Contractual incompleteness gives rise to two regimes, identified with make and buy. The performance measure on which comprehensive contracts can be written is imperfect in the sense of being subject to manipulation. The performance incentives faced by the agent are stronger in the "buy" regime. A positive (negative) impact -- or "externality" -- of manipulation on true performance favors make (buy).

Sequential Investments, Know-How Transmission, and Optimal Organization

Tsung-Sheng Tsai et al. — Thu, 01 Dec 2011 03:03:46 PST

In a two-stage sequential investment problem, a principal can use either a single agent or two separate agents to execute the project. The final outcome of the project depends upon both the agent's investments and the first-stage outcome. The principal wishes to stop the project when the first stage is a failure; however, she may not know the first-stage outcome, so that she has to pay the agent a rent to extract that information. Furthermore, the first-stage agent can transmit his know-how to the second-stage agent. Although there is a transmission cost under separate agency while there is no cost under single agency, single agency is not always optimal. This is because the transmission cost can reduce the agent's incentive to continue the project so that the information rent can be lower under separate agency. Hence, the principal may prefer separate agency more even when the transmission cost becomes larger.

When Two-Part Tariffs are Not Enough: Mixing with Nonlinear Pricing

Steffen Hoernig et al. — Wed, 19 Oct 2011 10:23:47 PDT

We determine explicitly the fully nonlinear equilibrium tariffs in a simple tractable model where two firms compete for consumers whose private preferences for products and quantities are correlated because they mix both goods. Contrary to the existing literature assuming uncorrelated preferences, neither full exclusivity nor two-part tariffs can arise in equilibrium. The equilibrium tariff sorts consumers through decreasing marginal prices even when goods are almost homogeneous. The market splits endogenously between one-stop and two-stop shopping customers. This conclusion also holds when consumers differ in total demand.