From Custer to Thermopylae: Last stand behavior in multi-stage contests

In a multi-stage contest known as a two-player race, players display two fundamental behaviors: (1) the laggard will make a last stand in order to avoid the cost of losing; and (2) the player who is ahead will defend his lead if it is threatened. Last stand behavior, in particular, contrasts with previous research where the underdog simply gives up. The distinctive results are achieved by introducing losing penalties and discounting into the racing environment. This framework permits the momentum effect, typically ascribed to the winner of early stages, to be more thoroughly examined. I study the likelihood that the underdog will catch up. I find that neck-and-neck races are common when the losing penalty is large relative to the winning prize, while landslide victories occur when the prize is relatively large. Closed-form solutions are given for the case where players have a common winning prize and losing penalty.     

Second chance offers versus sequential auctions: theory and behavior

Second chance offers in online marketplaces involve a seller conducting an auction for a single object and then using information from the auction to offer a losing bidder a take-it-or-leave-it price for another unit. We theoretically and experimentally investigate this practice and compare it to two sequential auctions. We show that the equilibrium bidding strategy in the second chance offer mechanism only exists in mixed strategies, and we observe that this mechanism generates more profit for the auctioneer than two sequential auctions. We also observe virtually no rejections of profitable offers in the ultimatum bargaining stage.      

Information aggregation in auctions with an unknown number of bidders

Information aggregation, a key concern for uniform-price, common-value auctions with many bidders, has been characterized in models where bidders know exactly how many rivals they face. A model allowing for uncertainty over the number of bidders is essential for capturing a critical condition for information to aggregate: as the numbers of winning and losing bidders grow large, information aggregates if and only if uncertainty about the fraction of winning bidders vanishes. It may be possible for the seller to impart this information by precommitting to a specified fraction of winning bidders, via a proportional selling policy. Intuitively, this could make the proportion of winners known, and thus provide all the information that bidders need to make winner's curse corrections.     

Selling options

Contracts often take the form of options: oil fields can be abandoned, planning permission may go unused, and acquired firms can be liquidated. We consider a seller who auctions a dynamic option among N agents. After the auction, the economy evolves and the winning bidder chooses both if and when to execute the option. The revenue-maximising auction consists of an up-front bid and a contingent fee, where the latter is chosen in a Pigouvian manner, so the winning agent's choice of exercise time maximises the seller's revenue. This contingent payment is time- and state-invariant, so the seller does not have to observe post-auction information in order to implement the optimal auction. The revenue-maximising mechanism induces a dynamic distortion: the option is exercised later than under the comparable welfare-maximising mechanism.     

Optimistic irrationality and overbidding in private value auctions

Bidding one’s value in a second-price, private-value auction is a weakly dominant solution (Vickrey in J Finance 16(1):8–37, 1961), but repeated experimental studies find more overbidding than underbidding. We propose a model of optimistically irrational bidders who understand that there are possible gains and losses associated with higher bids but who may overestimate the additional probability of winning and/or underestimate the potential losses when bidding above value. These bidders may fail to discover the dominant strategy—despite the fact that the dominant strategy only requires rationality from bidders—but respond in a common sense way to out-of-equilibrium outcomes. By varying the monetary consequences of losing money in experimental auctions we observe more overbidding when the cost to losing money is low, and less overbidding when the cost is high. Our findings lend themselves to models in which less than fully rational bidders respond systematically to out-of-equilibrium incentives, and we find that our model better fits the effects of our manipulations than most of the existing models we consider.     

The role of externalities and information aggregation in market collapse

We examine the role that belief, network externality, and information aggregation play in inefficient market collapses. After receiving consecutive negative shocks, some ex-ante identical Bayesian agents will be discouraged about the unknown state of the market they invest; therefore, they will stop investing. This decision will have two effects: first, it will cause agents to aggregate information through social/observational learning; second, it will decrease the network externality effect. We show that there might be an inefficient market collapse if the externality effect diminishes too much, and the cost of re-entry to the market is too high. We also analyze the effects of strategic delay and experimentation on the exit decision of the agents. I especially thank Thomas D. Jeitschko, Matthew Mitchell, B. Ravikumar Ted Temzelides. I also thank anonymous referees, an associate editor, John Conlon, Larry Samuelson, Troy Tassier, Stephen Williamson, and seminar participants of the University of Saskatchewan, Georgia Tech, Concordia University, University of Manitoba, Iowa Alumni Workshop, Midwest Economic Theory Conferences held at Indiana Bloomington, and Notre Dame, and 1st International Conference on Business, Management and Economics organized by Yasar University.     

The weak core of simple games with ordinal preferences: implementation in Nash equilibrium

In a simple game, coalitions belonging to a given class are “absolutely powerful” while others have no power. We attempt to make this distinction operational. Toward this end, we propose two axioms on social choice correspondences, Strong Non-Discrimination and Exclusion. Strong Non-Discrimination describes circumstances under which certain coalitions, the losing coalitions, have no influence over social choice. Exclusion requires that there are situations in which certain coalitions, the winning coalitions, can exercise their power. We show that the weak core correspondence is the minimal correspondence satisfying Maskin Monotonicity and Strong Non-Discrimination. We also show that the weak core is the unique correspondence satisfying Nash implementability, Strong Non-Discrimination, and Exclusion.     

The effect of randomized school admissions on voter participation

There is little causal evidence on the effect of economic and policy outcomes on voting behavior. This paper uses randomized outcomes from a school choice lottery to examine if lottery outcomes affect voting behavior in a school board election. We show that losing the lottery has no significant impact on overall voting behavior; however, among white families, those with above median income and prior voting history, lottery losers were significantly more likely to vote than lottery winners. Using propensity score methods, we compare the voting of lottery participants to similar families who did not participate in the lottery. We find that losing the school choice lottery caused an increase in voter turnout among whites, while winning the lottery had no effect relative to non-participants. Overall, our empirical results lend support to models of expressive and retrospective voting, where likely voters are motivated to vote by past negative policy outcomes.     

Fair Income Tax

In a model where agents have unequal skills and heterogeneous preferences over consumption and leisure, we look for the optimal tax on the basis of efficiency and fairness principles and under incentive-compatibility constraints. The fairness principles considered here are: (1) a weak version of the Pigou–Dalton transfer principle; (2) a condition precluding redistribution when all agents have the same skills. With such principles we construct and justify specific social preferences and derive a simple criterion for the evaluation of income tax schedules. Namely, the lower the greatest average tax rate over the range of low incomes, the better. We show that, as a consequence, the optimal tax should give the greatest subsidies to the working poor (the agents having the lowest skill and choosing the largest labour time).     

Help the Low Skilled or Let the Hardworking Thrive? A Study of Fairness in Optimal Income Taxation

In a model where agents have unequal wages and heterogeneous preferences, we study the optimal redistribution via an income tax, when the social objective is based on a combination of efficiency and fairness principles, and when incentive issues are taken into account. We show how some fairness principles entail specific features for the optimal taxes, such as progressivity or tax exemption for incomes below the minimum wage.     

Majority rule when voters like to win

I analyze symmetric majority rule voting equilibria when voters wish to elect the better candidate and to vote for the winner. When voters care only about the winning candidate (the standard formulation) a unique responsive equilibrium exists. The addition of a desire to win creates multiple equilibria, some with unusual properties. In most of these equilibria information is not aggregated effectively, and I uncover the novel possibility of negative information aggregation in which information aggregated in equilibrium is used to select the worse rather than the better candidate.I then characterize the efficiency of optimal equilibria as the population becomes large and show that a discontinuity arises in the information aggregation capabilities of the majority rule voting mechanism: in elections without a dominant front-running candidate the better candidate is almost surely elected, whereas in races with a front-runner information cannot be effectively aggregated in equilibrium.     

Asymptotic and small sample analysis of the stochastic properties and certainty equivalents of winning bids in independent private values auctions$\!$

Summary. This paper investigates the stochastic properties of the first price and second price winning bids in auctions with risk neutral bidders with independent and identically distributed valuations. In such an environment, the winning first price bids second order stochastically dominate the second price winning bids. A key result of this paper is that the ratio of the variance of the winning first price bid to that of the winning second price bid is strictly less than one even as the number of bidders goes to infinity. This suggests that the stochastic dominance of the winning first price bids does not vanish even in the limit. Both the asymptotic and small sample properties of winning bids are investigated. In particular, the small sample results suggest that the identification power of econometric procedures that rely on winning bids can decline rapidly as the number of bidders increases. This paper also includes a systematic evaluation of the difference in certainty equivalents between the two auction formats for several common distributions and number of bidders for the case of auctioneers with constant coefficient of absolute risk aversion. These results are presented in a form that makes it easy to apply them to a specific auction of interest.Received: 15 July 2002, Revised: 7 April 2003, JEL Classification Numbers: D44.I would like to thank David Pearce for helpful comments and discussion and a referee for suggestions that have greatly improved this paper.     

Majority rule when voters like to win

I analyze symmetric majority rule voting equilibria when voters wish to elect the better candidate and to vote for the winner. When voters care only about the winning candidate (the standard formulation) a unique responsive equilibrium exists. The addition of a desire to win creates multiple equilibria, some with unusual properties. In most of these equilibria information is not aggregated effectively, and I uncover the novel possibility of negative information aggregation in which information aggregated in equilibrium is used to select the worse rather than the better candidate.I then characterize the efficiency of optimal equilibria as the population becomes large and show that a discontinuity arises in the information aggregation capabilities of the majority rule voting mechanism: in elections without a dominant front-running candidate the better candidate is almost surely elected, whereas in races with a front-runner information cannot be effectively aggregated in equilibrium.     

Bidding for the unemployed: An application of mechanism design to welfare-to-work programs

This paper applies the theory of mechanism design to welfare-to-work programs. When procuring welfare-to-work projects to employment service providers, governments face the problems of adverse selection (the winning provider is not the most efficient one) and moral hazard (the winning provider shirks in its responsibility to reintegrate unemployed people). We compare the constant-reward second-price auction with the socially optimal mechanism and show that the auction generates social welfare that is close to the optimal mechanism, while requiring less information and weaker commitment.     

Implementing egalitarian-equivalent allocation of indivisible goods on restricted domains

Summary. We study the problem of allocating several units of homogeneous indivisible goods when monetary compensations are possible. First, we show that there is no strategy-proof, budget balanced, and egalitarian-equivalent mechanism even on extremely restricted preference domains. Next, we present two characterizations of strategy-proof and decision-efficient mechanisms that satisfy a stronger version of egalitarian-equivalence on preference domains bounded above. These characterizations tell us a trade-off between strategy-proofness and Pareto efficiency, and a relationship with strategy-proof and envy-free mechanisms. Finally, we prove that no egalitarian-equivalent mechanism is Nash implementable even on extremely restricted preference domains.Received: 22 April 2002, Revised: 17 February 2003, JEL Classification Numbers: C72, D63, D71, D82.I am very grateful to Naoki Yoshihara for useful discussions and suggestions that motivate me to study this subject. I would also like to thank Kotaro Suzumura, Koichi Tadenuma, Yoshikatsu Tatamitani, and the editor and two anonymous referees of this journal for helpful comments.     

Uniqueness of stationary equilibrium payoffs in coalitional bargaining

We study a model of sequential bargaining in which, in each period before an agreement is reached, the proposer?s identity is randomly determined, the proposer suggests a division of a pie of size one, each other agent either approves or rejects the proposal, and the proposal is implemented if the set of approving agents is a winning coalition for the proposer. The theory of the fixed point index is used to show that stationary equilibrium expected payoffs of this coalitional bargaining game are unique. This generalizes Eraslan [34] insofar as: (a) there are no restrictions on the structure of sets of winning coalitions; (b) different proposers may have different sets of winning coalitions; (c) there may be a positive probability that no proposer is selected.     

Simple Mechanisms to Implement the Core of College Admissions Problems

This paper analyzes simple mechanisms implementing (subselections of) the core correspondence of matching markets. We provide a sequential mechanism which mimics a matching procedure for many-to-one real life matching markets. We show that only core allocations should be attained when agents act strategically when faced with this mechanism. We also provide a second mechanism to implement the core correspondence in Subgame Perfect Equilibrium. Journal of Economic Literature Classification Numbers: C78, D78.     

An Experimental Study of the Disposition Effect: Evidence From Macau

The disposition effect-the tendency to sell winning transactions too soon and hold losing transactions too long-is examined experimentally in Macau. The findings show that the disposition effect exists strongly under the modified version of the experiment designed by Weber and Camerer [1998]. This study also points out that a psychological factor, the locus of control, can partly explain the disposition effect observed in this experiment.     

Minimally acceptable altruism and the ultimatum game

I suppose that people react with anger when others show themselves not to be minimally altruistic. With heterogeneous agents, this can account for the experimental results of ultimatum and dictator games. Moreover, it can account for the surprisingly large fraction of individuals who offer an even split with parameter values that are more plausible than those that are required to explain outcomes in these experiments with the models of Levine [Levine, D.K., 1998. Modeling altruism and spitefulness in experiments. Review of Economic Dynamics 1, 593–622], Fehr and Schmidt [Fehr, E., Schmidt, K.M., 1999. A theory of fairness, competition and cooperation. Quarterly Journal of Economics 114, 817–868], Dickinson [Dickinson, D.L., 2000. Ultimatum decision making: a test of reciprocal kindness. Theory and Decision 48, 151–177] and Bolton and Ockenfels [Bolton, G.E., Ockenfels, A., 2000. ERC: a theory of equity, reciprocity, and competition. American Economic Review 90, 166–193].     

INTENSITY OF COMPETITION, ENTRY AND ENTRY DETERRENCE IN RENT SEEKING CONTESTS

In rent seeking contests agents compete over a given amount of resource a prize. To increase the likelihood of winning the prize, the agents expend efforts. This paper addresses the issue of entry to and entry deterrence from rent seeking contest. The main purpose of the analysis is to provide an explanation for the empirical fact that the number of participants in contests is usually small. I also obtain results on the relationship between the intensity of competition in a contest and the amount of the contenders'expenditures.