The B.E. Journal of Theoretical Economics

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.

Strategy-Proof Compromises

Peter Postl — Fri, 07 Oct 2011 08:17:21 PDT

We study strategy-proof decision rules in the variant of the canonical public good model proposed by Borgers and Postl (2009). In this setup, we fully characterize the set of budget-balanced strategy-proof deterministic mechanisms, which are simple threshold rules. For smooth probabilistic mechanisms, we provide a necessary and sufficient condition for dominant strategy implementation. When allowing for discontinuities in the mechanism, our necessary condition remains valid, but additional conditions must hold for sufficiency. We also show that, among ex post efficient decision rules, only dictatorial ones are strategy-proof. While familiar in spirit, this result is not the consequence of any known result in the literature.

Implementation of the Core in College Admissions Problems When Colleagues Matter

Serkan Kucuksenel — Fri, 02 Sep 2011 14:45:00 PDT

This paper presents mechanisms implementing the core correspondence of many-to-one matching markets, such as college admissions problems, where the students have preferences over the other students who would attend the same college. We first present a sequential mechanism implementing the core. We then show that simple two-stage mechanisms, which mimics the real-life processes, cannot be used to implement the core correspondence in subgame perfect Nash equilibrium even with strong assumptions on agents’ preferences.

Strategic Choice of Preferences: the Persona Model

David Wolpert et al. — Sat, 27 Aug 2011 10:05:37 PDT

Recent work in several fields has established that humans can adopt binding “behavioral” preferences and convincingly signal those preferences to other humans, either via their behavior or via their body language / tone of voice. In this paper, we model the strategic implications of this ability. Our thesis is that through a person's lifetime they (perhaps subconsciously) learn what such signaled, binding behavioral preferences result in the highest value of their actual preferences, given the resultant behavior of other players. We argue that this “persona” model may explain why many interpersonal preferences have the particular form they do. As an illustration, we use the persona model to explain cooperation in non-repeated versions of the Prisoner's Dilemma (PD). We also provide quantitative predictions to distinguish this explanation of cooperation from simply assuming people have actual preferences biased towards cooperation. In particular, we show that the persona model predicts a “crowding out” phenomenon in the PD, in which introducing incentives to cooperate causes players to stop cooperating instead. We also use the persona model to predict a tradeoff between the robustness of cooperation in the PD and the benefit of that cooperation.

Transitional Dynamics in a Tullock Contest with a General Cost Function

Martin Grossmann et al. — Thu, 25 Aug 2011 12:43:43 PDT

This paper constructs and analyzes open-loop equilibria in an infinitely repeated Tullock contest in which two contestants contribute efforts to accumulate individual asset stocks over time. To investigate the transitional dynamics of the contest in the case of a general cost function, we linearize the model around the steady state. Our analysis shows that optimal asset stocks and their speed of convergence to the steady state crucially depend on the elasticity of marginal effort costs, the discount factor and the depreciation rate. In the case of a cost function with a constant elasticity of marginal costs, a lower discount factor, a higher depreciation rate and a lower elasticity imply a higher speed of convergence to the steady state. We further analyze the effects of second prizes in the contest. A higher prize spread increases individual and aggregate asset stocks, but does not alter the balance of the contest in the long run. During the transition, a higher prize spread increases asset stocks, produces a more balanced contest in each period and increases the speed of convergence to the steady state.

Multiproduct Duopoly with Vertical Differentiation

Yi-Ling Cheng et al. — Tue, 09 Aug 2011 09:36:30 PDT

This paper investigates a two-stage competition in a vertically differentiated industry, where each firm produces an arbitrary number of similar qualities and sells them to heterogeneous consumers. The number of products, qualities, prices, and the extent of the market coverage are endogenously determined. We show that when unit costs of quality improvement are increasing and quadratic, each firm has an incentive to provide a disconnected set of similar qualities approximating a continuum. The finding contrasts sharply with the single-quality outcome when the market coverage is exogenously determined. We also show that allowing for multiple qualities intensifies the level of competition, lowers the profit of each firm, and raises the consumer surplus and the social welfare in comparison to the single-quality duopoly.

A New Existence and Uniqueness Theorem for Continuous Games

Seamus D. Hogan — Thu, 04 Aug 2011 11:05:20 PDT

This paper derives a general sufficient condition for existence and uniqueness in continuous games using a variant of the contraction mapping theorem applied to mappings from a subset of the real line on to itself. We first prove this contraction mapping variant, and then show how the existence of a unique equilibrium in the general game can be shown by proving the existence of a unique equilibrium in an iterative sequence of games involving such mappings. Finally, we show how a general condition for this to occur is that a matrix derived from the Jacobian matrix of best-response functions has positive leading principal minors, and how this condition generalises some existing uniqueness theorems for particular games. In particular, we show how the same conditions used in those theorems to show uniqueness, also guarantee existence in games with unbounded strategy spaces.

The Survival Assumption in Intertemporal Economies

Jean-Marc Bonnisseau et al. — Wed, 08 Jun 2011 20:05:04 PDT

In an economy with a non-convex production sector, we provide an assumption on each individual producer, which implies that the survival assumption holds true at the aggregate level for general pricing rules. For the marginal pricing rule, we derive this assumption from the bounded marginal productivity of inputs. We apply this approach to intertemporal economies and we show how our assumption fits well with the time structure. We obtain a tractable existence result of equilibria for discrete time growth models.

Alliance Partner Choice in Markets with Vertical and Horizontal Externalities

Keisuke Hattori et al. — Wed, 08 Jun 2011 20:04:59 PDT

This study investigates the choice between complementary and parallel alliances in a market with vertical and horizontal externalities. One composite goods firm competes with two components producers, each providing a complementary component of a differentiated composite good. Although the joint profits from a parallel alliance between the composite goods firm and a components producer are always larger than those from a complementary alliance between components producers, through Nash bargaining, a components producer prefers the complementary (parallel) alliance when the degree of product differentiation is sufficiently large (small). Combined with the result that a complementary alliance is socially preferable, our findings provide meaningful implications for antitrust policy.

Intertemporal Bounded Rationality as Consideration Sets with Contraction Consistency

Dean Spears — Wed, 08 Jun 2011 20:04:53 PDT

How would a boundedly rational agent react to a larger menu? I model choice from an unobservable, subjective consideration subset. Consideration sets satisfy Sen’s property alpha: larger objective choice sets can generate smaller consideration sets. The contribution of this paper is a representation of choice among menus: choice sets are only as valuable as the best item in their subjective subsets, so larger sets can be worse. Unlike people facing temptation, a boundedly rational decision maker can strictly prefer both of two choice sets to their union. This model of intertemporal choice reflects how an agent who satisfies Weak WARP would choose, if sophisticated about her bounded rationality.

Symmetry or Dynamic Consistency?

Larry G. Epstein et al. — Wed, 08 Jun 2011 20:04:45 PDT

In a setting with repeated experiments, where evidence about the experiments is symmetric, a decision-maker ranks bets (or acts) over their outcomes. We describe a stark modeling trade-off between symmetry of preference (indifference to permutations), dynamic consistency and ambiguity. Then, assuming that experiments are ordered in time, we outline an axiomatic model of preference that exhibits dynamic consistency and yet models learning under ambiguity.

Stochastic Stability in Finitely Repeated Two Player Games

Jack Robles — Wed, 27 Apr 2011 08:04:39 PDT

We apply stochastic stability to undiscounted finitely repeated two player games without common interests. We prove an Evolutionary Feasibility Theorem as an analog to the Folk Theorem (Benoit and Krishna, 1985 and 1987). Specifically, we demonstrate that as repetitions go to infinity, the set of stochastically stable equilibrium payoffs converges to the set of individually rational and feasible payoffs. This derivation requires stronger assumptions than the Nash Folk Theorem (Benoit and Krishna, 1987). It is demonstrated that the stochastically stable equilibria are stable as a set, but unstable as individual equilibria. Consequently, the Evolutionary Feasibility Theorem makes no prediction more specific than the entire individually rational and feasible set.