Endogenous Prize Research Articles

Evolutionary Stability and Evolution of Misperceptions in Conflict

We find Evolutionary Stable Strategy (ESS) and Evolutionary Stable Preference (ESP) in conflict modeled as a pairwise contest game for an endogenous prize. Our study attributes overbidding under ESS to misperceptions about various attributes of rival players in a conflict that evolved through ESP. We show that players tend to over perceive the resource endowments of rival players and this, in turn, gives rise to the more aggressive behaviour of players under ESS. We also use the notion of conflict expenditure in an endogenous prize setting to show that the false perception about the rival players under ESP gives rise to higher levels of dissipation of resources into appropriation. JEL Classifications: D70, D72, D74

Stability of dynamic asymmetric contests with endogenous prizes

Repeated asymmetric contest games are examined under conditions which guarantee the existence and uniqueness of pure Nash equilibrium (Hirai and Szidarovszky 2013). Conditions are derived for the local asymptotical stability of the equilibrium under continuous and discrete dynamics with gradient adjustments. In both cases, a crucial assumption is the nonexistence of a dominant player at the equilibrium level. In the case of continuous time scales, this is sufficient for stability, and in the discrete case, the speeds of adjustments have to be sufficiently small. As special cases, symmetric and semi-symmetric games are analyzed.

Payoff-Improving Competition: Games with Negative Externalities

We demonstrate that more intense competition in games with production and negative externalities may be payoff-improving, and therefore welcomed by incumbents. In games that feature equilibria with strategic complements, increased competition may give rise to a new equilibrium where aggregate effort is lower, and the resulting reduced levels of externalities ultimately leaves all players better off. This setting applies to models of Cournot oligopoly, of common pool resources, and contests with endogenous prizes.

Contests over joint production on networks

AbstractWe consider a network of heterogeneous agents where each edge represents a two‐player contest between the respective nodes. In these bilateral contests, agents compete over an endogenous prize jointly produced using their own contest efforts. We provide a necessary and sufficient condition for the existence of Nash equilibrium and characterize the equilibrium total effort for every agent. Our model has insightful results regarding the network type, that is, depending on whether the network is bipartite or nonbipartite. Finally, considering the sum of all expected utilities as an efficiency notion, we investigate the optimal network structure.

A Model Of rivalries with endogenous prize and strength

This paper extends Beviá and Corchón (2013) to a model with both endogenous contestable prize and endogenous relative strength. Such a setting is ideal for the study of intra-organizational rivalries, commonly observed in family, sports, promotion, and duopoly. We find that when the game starts with asymmetric players, the weaker player exerts more effort than the stronger player. As a result, the weaker player partially overcomes the disadvantage of being weak. In this setting, neither domino nor avalanche effect exists.

Asymmetric endogenous prize contests

We consider a two-player contest in which one contestant has a headstart advantage, but both can exert further effort. We allow the prize to depend on total performance in the contest and consider the respective cases in which efforts are productive and destructive of prize value. When the contest success function takes a logit form, and marginal cost is increasing in effort, we show that a Nash equilibrium exists and is unique both in productive and destructive endogenous prize contests. In equilibrium, the underdog expends more resources to win the prize, but still his probability of winning remains below that of the favorite. In a productive contest, the underdog behaves more aggressively and wins the prize more often in comparison to a fixed-value contest. Thus, the degree of competitive balance—defined as the level of uncertainty of the outcome—depends upon the (fixed or endogenous) prize nature of the contest.

Does Manufacturer Advertising Crowd‐in or Crowd‐out Retailer Advertising? An Application of an Endogenous Prize Contest with Asymmetric Players

When a manufacturer advertises, what is the impact on retailer advertising? I analyze a contest model of advertising where total advertising by the manufacturer and by retailers determines market size, and the relative level of advertising by each retailer determines market share. If retailers are symmetric I show that there is a crowding‐in effect so increased manufacturer advertising increases retail advertising. But if one retailer is stronger, then marginal increases in manufacturer advertising have a crowding‐out effect on retailer advertising, while sufficiently large increases have a crowding‐in effect by “jump‐starting” competition between retailers for the larger market. Furthermore, asymmetric abilities in such contests can lead the weaker player to effectively drop out of the contest, thereby undermining the ability of increased prizes to increase effort by intensifying competition.

EXISTENCE AND UNIQUENESS OF EQUILIBRIUM IN ASYMMETRIC CONTESTS WITH ENDOGENOUS PRIZES

This paper considers contests in which the efforts of the players determine the value of the prize. Players may have different valuations of the prize and different abilities to convert expenditures to productive efforts. In addition, players may face different financial constraints. This paper presents a proof for the existence and uniqueness of a pure Nash equilibrium in asymmetric contests with endogenous prizes.

All-Pay Auctions: Implementation and Optimality

This paper analyzes how all-pay auctions with endogenous prizes can be used to provide effort incentives. We show that wide classes of effort distributions can be implemented as equilibrium outcomes of such games. We also ask how all-pay auctions have to be structured so as to induce high expected highest efforts without generating excessive wasteful efforts of losers. All-pay auctions with endogenous prizes can do better than all-pay auctions with fixed prizes in this respect, in particular, when the prize function is approximately linear. We use the results to compare patents and prizes as innovation incentives, and to explore promotion incentives in organizations.

Does Manufacturer Advertising Crowd-In or Crowd-Out Retailer Advertising? An Application of an Endogenous Prize Contest with Asymmetric Players

When a manufacturer advertises, what is the impact on retailer advertising? I analyze a contest model of advertising where total advertising by the manufacturer and by retailers determines market size, and the relative level of advertising by each retailer determines market share. If retailers are symmetric I show that there is a crowding-in effect so increased manufacturer advertising increases retail advertising. But if one retailer is stronger, then marginal increases in manufacturer advertising have a crowding-out effect on retailer advertising, while sufficiently large increases have a crowding-in effect by jump-starting competition between retailers for the larger market. Furthermore, asymmetric abilities in such contests can lead the weaker player to effectively drop out of the contest, thereby undermining the ability of increased prizes to increase effort by intensifying competition. More generally the model can be applied to other contests such as patent races or promotion tournaments where not just the probability of winning but also the value of winning depends on contest effort levels.

The All-Pay Auction with Non-Monotonic Payoff

We analyse an endogenous prize all-pay auction under complete information where it is possible that none of the bidders wins and the winning payoff becomes non-monotonic in own bid. We derive the conditions for the existence of pure strategy equilibria and fully characterize the unique mixed strategy equilibrium when pure strategy equilibria do not exist. The highvaluation bidder places two distinct mass points in his equilibrium mixed strategy and the equilibrium support of the low-valuation bidder is not continuous. Under common valuation, in the equilibrium mixed strategy both bidders place mass points at the same point of the support. Possible applications are discussed.

Innovation contests with temporary and endogenous monopoly rents

In this article, a Tullock contest success function is used to model an innovation contest with endogenous innovation height. We can prove stability for this endogenous prize contest. The winner of the contest gains a monopoly rent, which has two dimensions. In the first dimension the winning firm influences the innovation height. The second dimension is the life span of the temporary monopoly. This life span is determined by the contest designer, who can be a social planner or the consumers. We find interior solutions in both cases, whereas consumers prefer a monopoly life span below the social optimum. Furthermore, the optimal number of firms in the contest is two.

All-Pay Auctions with Negative Prize Externalities: Theory and Experimental Evidence

The paper characterizes the mixed-strategy equilibria in all-pay auctions with endogenous prizes that depend positively on own effort and negatively on the effort of competitors. Such auctions arise naturally in the context of investment games, lobbying games, and promotion tournaments. We also provide an experimental analysis of a special case which captures the strategic situation of a two-stage game with investment preceding homogenous Bertrand competition. We obtain overinvestment both relative to the mixed-strategy equilibrium and the social optimum.

Incentives in Tournaments with Endogenous Prize Selection

Tournament incentive schemes offer payments dependent on relative performance and are intended thereby to motivate agents to exert productive effort. Unfortunately, however, an agent may also be tempted to degrade the production of his competitors in order to improve the own relative position. We investigate whether this sabotage problem is mitigated in a repeated interaction between the agents and the principal. As sabotage can hardly be observed in real-world organizations, we employ a controlled experiment. Our data provide clear evidence that agents' behavior is not only guided by competition between agents but also by the possibility of punishing the principal via sabotage.

Incentives in Tournaments with Endogenous Prize Selection

Tournament incentive schemes offer payments dependent on relative performance and thereby are intended to motivate agents to exert productive effort. Unfortunately, however, an agent may also be tempted to destroy the production of his competitors in order to improve the own relative position. In the present study we investigate whether this sabotage problem is mitigated in a repeated interaction between the agents and the principal. As sabotage can hardly be observed in real-world organizations we employ a controlled experiment. Our data provide clear evidence that agents' behavior is not only guided by competition between agents but also by the possibility to punish the principal via sabotage.