All-pay auction equilibria in contests

We analyze (non-deterministic) contests with anonymous contest success functions. There is no restriction on the number of contestants or on their valuations for the prize. We provide intuitive and easily verifiable conditions for the existence of an equilibrium with properties similar to the one of the (deterministic) all-pay auction. Since these conditions are fulfilled for a wide array of situations, the predictions of this equilibrium are very robust to the specific details of the contest. An application of this result contributes to fill a gap in the analysis of the popular Tullock rent- seeking game because it characterizes properties of an equilibrium for increasing returns to scale larger than two, for any number of contestants and in contests with or without a common value. Keywords: (non-) deterministic contest, all-pay auction, contest success functions. JEL Classification Numbers: C72 (Noncooperative Games), D72 (Economic Models of Political Processes: Rent-Seeking, Elections), D44 (Auctions).

Foundations for contest success functions

In the literature the outcome of contests is either interpreted as win probabilities or as shares of the prize. With this in mind, we examine two approaches to contest success functions. In the first we analyze the implications of contestants' incomplete information concerning the "type" of the contest administrator. While in the case of two contestants this approach can rationalize prominent contest success functions, we show that it runs into difficulties when there are more agents. Our second approach interprets contest success functions as sharing rules and establishes a connection to bargaining and claims problems which is independent of the number of contestants. Both approaches provide foundations for popular contest success functions and guidelines for the definition of new ones. Keywords: Endogenous Contests, Contest Success Function. JEL Classification: C72 (Noncooperative Games), D72 (Economic Models of Political Processes: Rent-Seeking, Elections), D74 (Conflict; Conflict Resolution; Alliances).

The Complete Information First. Price Auction or the Importance of Being Indivisible

Abstract Despite the popularity of auction theoretical thinking, it appears that no one has presented an elementary equilibrium analysis of the first-price sealed-bid auction mechanism under complete information. This paper aims to remedy that omission. We show that the existence of pure strategy undominated Nash equilibria requires that the bidding space is not "too divisible" (that is, a continuum). In fact, when bids must form part of a finite grid there always exists a "high price equilibrium". However, there might also be "low price equilibria" and when the bidding space is very restrictive the revenue obtained in these "low price equilibria" might be very low. We discuss the properties of the equilibria and an application of auction theoretical thinking in which "low price equilibria" may be relevant. Keywords: First-price auctions, undominated Nash equilibria. JEL Classification Numbers: C72 (Noncooperative Games), D44 (Auctions).

Welfare Maximizing Contest Success Functions when the Planner Cannot Commit

We analyze how a contest organizer chooses optimally the winner when the contestants' efforts are already exerted and commitment to the use of a given contest success function is not possible. We de…ne the notion of rationalizability in mixed-strategies to capture such a situation. Our approach allows to derive different contest success functions depending on the aims and attitudes of the decider. We derive contest success functions which are closely related to commonly used functions providing new support for them. By taking into account social welfare considerations our approach bridges the contest literature and the recent literature on political economy. Keywords: Endogenous Contests, Contest Success Function, Mixed-Strategies. JEL Classi…cation: C72 (Noncooperative Games), D72 (Economic Models of Political Processes: Rent-Seeking, Elections), D74 (Conflict; Conflict Resolution; Alliances)

Signaling in Dynamic Contests: Some Impossibility Results

General signaling results in dynamic Tullock contests have been missing for long. The reason is the tractability of the problems. In this paper, an uninformed contestant with valuation vx competes against an informed opponent with valuation, either high vh or low vl. We show that; (i) When the hierarchy of valuations is vh ≥ vx ≥ vl, there is no pooling. Sandbagging is too costly for the high type. (ii) When the order of valuations is vx ≥ vh ≥ vl, there is no separation if vh and vl are close. Sandbagging is cheap due to the proximity of valuations. However, if vh and vx are close, there is no pooling. First period cost of pooling is high. (iii) For valuations satisfying vh ≥ vl ≥ vx, there is no separation if vh and vl are close. Bluffing in the first period is cheap for the low valuation type. Conversely, if vx and vl are close there is no pooling. Bluffing in the first stage is too costly. JEL: C72, C73, D44, D82. KEYWORDS: Signaling, Dynamic Contests, Non-existence, Sandbag Pooling, Bluff Pooling, Separating

Competition for Procurement Shares

We propose a new procurement procedure which allocates shares of the total amount to be procured depending on the bids of suppliers. Among the properties of the mechanism are: (i) Bidders have an incentive to par- ticipate in the procurement procedure, as equilibrium payoffs are strictly positive. (ii) The mechanism allows to vary the extent to which affirma- tive action objectives, like promoting local industries, are pursued. (iii) Surprisingly, even accomplishing affirmative action goals, procurement ex- penditures might be lower than under a classical auction format. Keywords: Procurement Auction, Affirmative Action. JEL: C72, D44, H57

A Folk Theorem for Games when Frequent Monitoring Decreases Noise

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 _. 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., _. 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 _. 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. JEL: C72/73, D82, L20. KEYWORDS: Repeated Games, Frequent Monitoring, Public Monitoring, Brownian Motion.

Direct and indirect subsidies in markets with system goods in the presence of externalities. Preliminary version

This paper derives a model of markets with system goods and two technological standards. An established standard incurs lower unit production costs but causes a negative externality. The paper derives the conditions for policy intervention and compares the effect of direct and indirect cost-reducing subsidies in two markets with system goods in the presence of externalities. If consumers are committed to the technology by purchasing one of the components, direct subsidies are preferable. For a medium-low cost difference between technological standards and a low externality cost it is optimal to provide a direct subsidy only to the first technology adopter. As the higher the externality cost raises, the more technology adopters should be provided with direct subsidies. This effect is robust in all extensions. In the absence of consumers commitment to a technological standard indirect and direct subsidies are both desirable. In this case, the subsidy to the first adopter is lower then the subsidy to the second adopter. Moreover, for the low cost difference between technological standards and low externality cost the fi rst fi rm chooses a superior standard without policy intervention. Finally, a perfect compatibility between components based on different technological standards enhances an advantage of indirect subsidies for medium-high externality cost and cost difference between technological standards. Journal of Economic Literature Classi fication Numbers: C72, D21, D40, H23, L13, L22, L51, O25, O33, O38. Keywords: Technological standards; complementary products; externalities; cost-reducing subsidies; compatibility.

The Lottery Blotto Game

In this paper we relax the Colonel Blotto game assumption that for a given battle the player who allocates the higher measure of resources wins that battle. We assume that for a given battle, the Colonel who allocates the higher measure of resources is more likely to win that battle. We have a simpler model for which we are able to compute all Nash equilibria in pure strategies for any valuations pro le that players might have. Something that is not possible for the original Blotto game. JEL: C72, D74, H56. KEYWORDS: Colonel Blotto game; lottery contest function.

Energy substrate used by workers of leaf-cutting ants during nest excavation

Energy substrate used by workers of leaf-cutting ants during nest excavation. In this study we aimed to ascertain whether leaf-cutting ant workers lose body reserves (fat or sugars) as a function of nest excavation. For each treatment, we isolated 10 workers of Atta sexdens into two experimental groups, Control (C- without excavation) and Soil (S- with excavation), which were kept for different time intervals (0, 24, 48 or 72 hours), totaling 700 tested workers. We then determined the concentration of soluble carbohydrates and total lipid content in them. The total carbohydrates were determined colorimetrically, based on the reaction between carbohydrates and sulfuric acid-phenol. For determination of lipids, the insects were immersed in organic solvent until they reached a constant weight. Our results showed that carbohydrates are consumed during nest excavation activities. In the experimental groups S24, S48 and S72, there was an average reduction of 5.82 (20.42%), 14.31 (44.96%) and 13.27 (43.96%) µ.mg-1 in soluble sugar when compared with the experimental groups that did not excavate. Furthermore, the lipids were not used during this activity. With respect to dry mass of the workers, their values were C0 = 8%, C24 = 10.4%, C48 = 9.2%, C72 = 10%, S24 = 9.2%, S48 = 8.7% and S72 = 8.5%. Our results show experimentally that the source of energy for nest excavation is carbohydrates, whereas lipids are conserved for other activities.

Affirmative Action through Extra Prizes

Some affirmative action policies establish that a set of disadvantaged competitors has access to an extra prize. Examples are gender quotas or a prize for national competitors in an international competition. We analyse the effects of creating an extra prize by reducing the prize in the main competition. Contestants differ in ability and agents with relatively low ability belong to a disadvantaged minority. All contestants compete for the main prize, but only disadvantaged agents can win the extra prize. We show that an extra prize is a powerful tool to ensure participation of disadvantaged agents. Moreover, for intermediate levels of the disadvantage of the minority, introducing an extra prize increases total equilibrium effort compared to a standard contest. Thus, even a contest designer not interested in affirmative action might establish an extra prize in order to enhance competition. Keywords: Asymmetric contest, equality of opportunity, affirmative action, discrimination, prize structure, exclusion principle. JEL: C72, D72, I38, J78

A Carrot and Stick Approach to Agenda-Setting

This paper models a legislature in which the same agenda setter serves for two periods, showing how he can exploit a legislature (completely) in the first period by promising future benefits to legislators who support him. In equilibrium, a large majority of legislators vote for the first-period proposal because they thereby maintain the chance of belonging to the minimum winning coalition in the future. Legislators may therefore approve policies by large majorities, or even unanimously, that benefit few, or even none, of them. The results are robust; but institutional arrangements (such as entitlements) can reduce the agenda setter's power by reducing his discretion to reward and punish legislators, and rules (such as sequential voting) can increase a legislator's ability to resist exploitation. Keywords: Legislative bargaining, distributive politics, agenda-setting, proposal power. JEL C72, D72, D78.

Moral Hazard in Repeated Procurement of Services

This paper analyzes repeated procurement of services as a four-stage game divided into two periods. In each period there is (1) a contest stage à la Tullock in which the principal selects an agent and (2) a service stage in which the selected agent provides a service. Since this service effort is non-verifiable, the principal faces a moral hazard problem at the service stages. This work considers how the principal should design the period-two contest to mitigate the moral hazard problem in the period-one service stage and to maximize total service and contest efforts. It is shown that the principal must take account of the agent's past service effort in the period-two contest success function. The results indicate that the optimal way to introduce this `bias' is to choose a certain degree of complementarity between past service and current contest efforts. This result shows that contests with `additive bias' (`multiplicative bias') are optimal in incentive problems when effort cost is low (high). Furthermore, it is shown that the severity of the moral hazard problem increases with the cost of service effort (compared to the cost of contest effort) and the number of agents. Finally, the results are extended to more general contest success functions. JEL classification: C72; D82 Key words: Biased contests; Moral Hazard; Repeated Game; Incentives.

Cooperative VS. Non-cooperative Truels: Little Agreement, but Does that Matter?

It is well-known that non-cooperative and cooperative game theory may yield different solutions to games. These differences are particularly dramatic in the case of truels, or three-person duels, in which the players may fire sequentially or simultaneously, and the games may be one-round or n-round. Thus, it is never a Nash equilibrium for all players to hold their fire in any of these games, whereas in simultaneous one-round and n-round truels such cooperation, wherein everybody survives, is in both the a -core and ß -core. On the other hand, both cores may be empty, indicating a lack of stability, when the unique Nash equilibrium is one survivor. Conditions under which each approach seems most applicable are discussed. Although it might be desirable to subsume the two approaches within a unified framework, such unification seems unlikely since the two approaches are grounded in fundamentally different notions of stability.

The Ghost in the Machine: Inferring Machine-Based Strategies from Observed Behavior

We introduce a procedure to infer the repeated-game strategies that generate actions in experimental choice data. We apply the technique to set of experiments where human subjects play a repeated Prisoner's Dilemma. The technique suggests that two types of strategies underly the data.