# 2011 Abstracts

## Center for Theoretical Economics

## 2011 Kansas Workshop on Economic Theory -- Abstracts of Papers |

We prove the existence of pure strategy Nash equilibria under very weak conditions of lower semi-continuity and quasi-concavity. Our results generalize previous results by Baye, Tian and Zhou as well as more recent results by Kim and Kum, Hou and Chang. We use the new results to establish the existence of pure strategy equilibria for games with discontinuous and non-quasi-concave payoffs such as probabilistic spatial voting games on the real line.
We consider the two-date model of a financial exchange economy (E,F ), with agents’ portfolio restrictions either represented by finitely many linear inequality constraints or satisfying Hart (1974)’s Weak No Market Arbitrage condition. The economy (E,F ) is shown to have the same consumption equilibria as a reduced economy (E,F'); for which the set of admissible portfolio allocations is bounded. Building upon the equilibrium existence result for reduced financial economies (E,F') (Aouani and Cornet, 2009), we then deduce the existence of equilibra of (E,F ) under standard assumptions on the consumption side and under the forementioned assumption on the financial side.
Consider a first-price, sealed-bid auction where participants have affiliated valuations and private budget constraints; that is, bidders have private multidimensional types. This article gives sufficient conditions for the existence of a monotone equilibrium in this setting and it offers an equilibrium characterization. Hard budget constraints introduce two competing effects on bidding. The direct effect depresses bids as participants hit their spending limit. The strategic effect encourages more aggressive bidding by participants with large budgets. Together these effects can yield discontinuous equilibrium strategies stratifying competition along the budget dimension. The strategic consequences of private budget constraints can be a serious confound in interpreting bidding behavior in auctions.
We study a dynamic global game with frictions in which agents privately learn about a fixed payoff parameter and repeatedly adjust their investment positions. The model has a rich structure of externalities: payoffs may depend on the volume of aggregate investment, on the concentration of investment, or on its volatility. We examine how small frictions similar to the Tobin tax affect equilibrium. The model exhibits a robust invariance result: the volume of aggregate investment measured in a pivotal contingency is invariant to a large family of frictions. Using the invariance result, we present setups in which a Tobin tax decreases the volatility of investment without compromising its volume.
The order and lattice structure of the equilibrium set in games with strategic complements do not survive a minimal introduction of strategic substitutes: in a lattice game in which all-but-one players exhibit strategic complements (with one player exhibiting strict strategic complements), and the remaining player exhibits strict strategic substitutes, no two equilibria are comparable. More generally, in a lattice game, if either (1) just one player has strict strategic complements and another player has strict strategic substitutes, or (2) just one player has strict strategic substitutes and has singleton-valued best-responses, then without any restrictions on the strategic interaction among the other players, no two equilibria are comparable. In such cases, the equilibrium set is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. Moreover, in such cases, with linearly ordered strategy spaces, the game has at most one symmetric equilibrium. Several examples are presented.
We study a decision maker who gradually learns the utility of available alternatives.This learning process is interrupted when a choice must be made. From the observer’s perspective, this formulation yields a random choice model. We propose and analyze one such learning process, the Bayesian Probit Process. We apply our model to the similarity puzzle: Tversky’s similarity hypothesis asserts that if two options, x and y have roughly equal utility and z is similar to x then making z available will reduce the probability of choosing x more than it reduces the probability of choosing y. However, there is also evidence that introducing a similar but inferior z may hurt y more than x and can even increase the probability of choosing x (attraction effect). We provide a definition of similarity based only on the random choice process and show that z is more like x than y if and only if the correlation between z and x’s signals is larger than the correlation between z and y’s signals. Our main result establishes that when z and x are correlated and sufficiently close in utility, introducing z hurts y more than x and may even increase the probability of choosing x early in the learning process, but eventually hurts x more than y. Hence, the attraction effect arises when the decision maker is relatively uninformed, while Tversky’s hypothesis holds when she becomes sufficiently familiar with the options. We then show that if z is similar to x and sufficiently inferior, the attraction effect never disappears.
Heifetz and Neeman (2006) show that, contrary to the classical result due to Crémer and McLean (1988), full surplus extraction (FSE) is generically impossible. Heifetz and Neeman's key observation is that FSE is possible only when priors satisfy the beliefs-determining-preferences (BDP) property due to Neeman (2004) and BDP priors are nongeneric in a geometric sense and a measure-theoretic sense. In this paper, we show instead that FSE is generically possible in the natural weak topology on priors. Our result differs from the Heifetz-Neeman genericity result in two aspects. First, our result does not rely on the notion of BDP priors which are in fact generic under our topological notion of genericity. Instead, we exploit a robustness property of the mechanism employed by Crémer and McLean (1988): when FSE is possible for a prior using a Cremer-McLean mechanism, it must be approximately possible in another Cremer-McLean mechanism for all nearby priors. Second, our result does not rely on convex combination on priors which is associated with the modeler's uncertainty about the information structure and is incompatible with Crémer and McLean (1988).
I explicitly derive the optimal dynamic incentive contract in a general continuous-time agency problem where inducing static first-best action is not always optimal. My framework generates two dynamic contracts new to the literature: (1) a “quiet-life" arrangement and (2) a suspension-based endogenously renegotiating contract. Both contractual forms induce a mixture of first-best and non-first-best action. These contracts capture common features in many real life arrangements such as “up-or-out", partnership, tenure, hidden compensation and suspension clauses. In applications, I explore the effects of taxes, bargaining and renegotiation on optimal contracting. My technical work produces a new type of incentive scheme I call sticky incentives which underlies the optimal, infrequent-monitoring approach to inducing a mixture of first-best and non-first-best action. Furthermore, I show how differences in patience between the principal and agent factor into optimal contracting. |