We study two-sided matching contests with two sets, A and B, each of which includes a finite numb... more We study two-sided matching contests with two sets, A and B, each of which includes a finite number of heterogeneous agents with commonly known types. The agents in each set compete in a lottery (Tullock) contest, and then are assortatively matched, namely, the winner of set A is matched with the winner of set B and so on until all the agents in the set with the smaller number of agents are matched. Each agent has a match value that depends on their own type and the type of their match. We assume that the agents’ efforts do not affect their match values and that they have a positive effect on welfare. Therefore, an interior equilibrium in which at least some of the agents are active is welfare superior to a corner equilibrium in which the agents choose to be non-active. We analyze the conditions under which there exists a (partial) interior equilibrium where at least some of the agents compete against each other and exert positive efforts.
We study all-pay auctions under incomplete information in which contestants have non-linear effor... more We study all-pay auctions under incomplete information in which contestants have non-linear effort functions. The designer offers the option of insurance for which a contestant pays a premium to the contest designer. If a contestant does not win he is reimbursed the cost of his effort. We demonstrate that contests with insurance may be profitable for a designer who wishes to maximize his expected revenue as based on the contestants’ expected total effort, the premium of the insured contestants, and their reimbursement.
We study two-player all-pay contests in which there is a positive probability of a tied outcome. ... more We study two-player all-pay contests in which there is a positive probability of a tied outcome. We show that the players' efforts in equilibrium do not depend on the expected prize in the case of a tie given that this prize is smaller than the prize for winning. The implications of this result are twofold. First, in symmetric one-stage contests, the designer who wishes to maximize the expected total effort should not award a prize in the case of a tie which is larger than one-third of the prize for winning. Second, in multi-stage contests, the designer should not limit the number of stages (tie-breaks) but should allow the contest to continue until a winner is decided.
We study two-stage all-pay contests where there is synergy between the stages. The reward for eac... more We study two-stage all-pay contests where there is synergy between the stages. The reward for each contestant is fixed in the first stage while it is effort-dependent in the second one. We assume that a player's effort in the first stage either increases (positive synergy) or decreases (negative synergy) his reward in the second stage. The subgame perfect equilibrium of this contest is analyzed with either positive or negative synergy. We show, in particular, that whether the contestants are symmetric or asymmetric their expected payoffs may be higher under negative synergy than under positive synergy. Consequently, they prefer smaller rewards (negative synergy) over higher ones (positive synergy).
We study two-sided matching contests with two sets of agents, each of which includes n heterogene... more We study two-sided matching contests with two sets of agents, each of which includes n heterogeneous agents with commonly known types. In the first stage, the agents simultaneously send their costly efforts and then the order of choosing a partner from the other set is determined according to the Tullock contest success function. In the second stage, each agent chooses a partner from the other set, and an agent has a positive revenue if there is a matching in which he chooses a partner from the other set and this partner also chooses him. We analyze the agents' equilibrium efforts in the first stage as well as their choices of partners in the second stage, and demonstrate that if the agents' values, which are functions of the types of the agents who are matched, are either multiplicative or additive, their efforts are not necessarily monotonically increasing in their types.
We study best-of-three all-pay auctions with two players who compete in three stages with a singl... more We study best-of-three all-pay auctions with two players who compete in three stages with a single match per stage. The first player to win two matches wins the contest. We assume that a prize sum is given, and show that if players are symmetric, the allocation of prizes does not have any effect on the players’ expected total effort. On the other hand, if players are asymmetric, in order to maximize the players’ expected total effort, independent of the players’ types, it is not optimal to allocate a single final prize to the winner. Instead, it is optimal to allocate intermediate prizes in the first stage or/and in the second stage in addition to the final prize. When the asymmetry of the players’ types is sufficiently high, it is optimal to allocate intermediate prizes in both two first stages and a final prize to the winner.
We study a contest with multiple, nonidentical prizes. Participants are privately informed about ... more We study a contest with multiple, nonidentical prizes. Participants are privately informed about a parameter (ability) affecting their costs of effort. The contestant with the highest effort wins the first prize, the contestant with the second-highest effort wins the second prize, and so on until all the prizes are allocated. The contest's designer maximizes expected effort. When cost functions are linear or concave in effort, it is optimal to allocate the entire prize sum to a single “first” prize. When cost functions are convex, several positive prizes may be optimal. (JEL D44, J31, D72, D82)
A contest architecture specifies how the contestants are split among several sub-contests whose w... more A contest architecture specifies how the contestants are split among several sub-contests whose winners compete against each other (while other players are eliminated). We compare the performance of such dynamic schemes to that of static winner-take-all contests from the point of view of a designer who maximizes either the expected total effort or the expected highest effort. For the case of a linear cost of effort, our main results are: 1) If the designer maximizes expected total effort, the optimal architecture is a single grand static contest. 2) If the designer maximizes the expected highest effort, and if there are sufficiently many competitors, it is optimal to split the competitors in two divisions, and to have a final among the two divisional winners. Finally, if the effort cost functions are convex, the designer may benefit by splitting the contestants into several sub-contests, or by awarding prizes to all finalists.
We study two-sided matching contests with two sets, A and B, each of which includes a finite numb... more We study two-sided matching contests with two sets, A and B, each of which includes a finite number of heterogeneous agents with commonly known types. The agents in each set compete in a lottery (Tullock) contest, and then are assortatively matched, namely, the winner of set A is matched with the winner of set B and so on until all the agents in the set with the smaller number of agents are matched. Each agent has a match value that depends on their own type and the type of their match. We assume that the agents’ efforts do not affect their match values and that they have a positive effect on welfare. Therefore, an interior equilibrium in which at least some of the agents are active is welfare superior to a corner equilibrium in which the agents choose to be non-active. We analyze the conditions under which there exists a (partial) interior equilibrium where at least some of the agents compete against each other and exert positive efforts.
We study all-pay auctions under incomplete information in which contestants have non-linear effor... more We study all-pay auctions under incomplete information in which contestants have non-linear effort functions. The designer offers the option of insurance for which a contestant pays a premium to the contest designer. If a contestant does not win he is reimbursed the cost of his effort. We demonstrate that contests with insurance may be profitable for a designer who wishes to maximize his expected revenue as based on the contestants’ expected total effort, the premium of the insured contestants, and their reimbursement.
We study two-player all-pay contests in which there is a positive probability of a tied outcome. ... more We study two-player all-pay contests in which there is a positive probability of a tied outcome. We show that the players' efforts in equilibrium do not depend on the expected prize in the case of a tie given that this prize is smaller than the prize for winning. The implications of this result are twofold. First, in symmetric one-stage contests, the designer who wishes to maximize the expected total effort should not award a prize in the case of a tie which is larger than one-third of the prize for winning. Second, in multi-stage contests, the designer should not limit the number of stages (tie-breaks) but should allow the contest to continue until a winner is decided.
We study two-stage all-pay contests where there is synergy between the stages. The reward for eac... more We study two-stage all-pay contests where there is synergy between the stages. The reward for each contestant is fixed in the first stage while it is effort-dependent in the second one. We assume that a player's effort in the first stage either increases (positive synergy) or decreases (negative synergy) his reward in the second stage. The subgame perfect equilibrium of this contest is analyzed with either positive or negative synergy. We show, in particular, that whether the contestants are symmetric or asymmetric their expected payoffs may be higher under negative synergy than under positive synergy. Consequently, they prefer smaller rewards (negative synergy) over higher ones (positive synergy).
We study two-sided matching contests with two sets of agents, each of which includes n heterogene... more We study two-sided matching contests with two sets of agents, each of which includes n heterogeneous agents with commonly known types. In the first stage, the agents simultaneously send their costly efforts and then the order of choosing a partner from the other set is determined according to the Tullock contest success function. In the second stage, each agent chooses a partner from the other set, and an agent has a positive revenue if there is a matching in which he chooses a partner from the other set and this partner also chooses him. We analyze the agents' equilibrium efforts in the first stage as well as their choices of partners in the second stage, and demonstrate that if the agents' values, which are functions of the types of the agents who are matched, are either multiplicative or additive, their efforts are not necessarily monotonically increasing in their types.
We study best-of-three all-pay auctions with two players who compete in three stages with a singl... more We study best-of-three all-pay auctions with two players who compete in three stages with a single match per stage. The first player to win two matches wins the contest. We assume that a prize sum is given, and show that if players are symmetric, the allocation of prizes does not have any effect on the players’ expected total effort. On the other hand, if players are asymmetric, in order to maximize the players’ expected total effort, independent of the players’ types, it is not optimal to allocate a single final prize to the winner. Instead, it is optimal to allocate intermediate prizes in the first stage or/and in the second stage in addition to the final prize. When the asymmetry of the players’ types is sufficiently high, it is optimal to allocate intermediate prizes in both two first stages and a final prize to the winner.
We study a contest with multiple, nonidentical prizes. Participants are privately informed about ... more We study a contest with multiple, nonidentical prizes. Participants are privately informed about a parameter (ability) affecting their costs of effort. The contestant with the highest effort wins the first prize, the contestant with the second-highest effort wins the second prize, and so on until all the prizes are allocated. The contest's designer maximizes expected effort. When cost functions are linear or concave in effort, it is optimal to allocate the entire prize sum to a single “first” prize. When cost functions are convex, several positive prizes may be optimal. (JEL D44, J31, D72, D82)
A contest architecture specifies how the contestants are split among several sub-contests whose w... more A contest architecture specifies how the contestants are split among several sub-contests whose winners compete against each other (while other players are eliminated). We compare the performance of such dynamic schemes to that of static winner-take-all contests from the point of view of a designer who maximizes either the expected total effort or the expected highest effort. For the case of a linear cost of effort, our main results are: 1) If the designer maximizes expected total effort, the optimal architecture is a single grand static contest. 2) If the designer maximizes the expected highest effort, and if there are sufficiently many competitors, it is optimal to split the competitors in two divisions, and to have a final among the two divisional winners. Finally, if the effort cost functions are convex, the designer may benefit by splitting the contestants into several sub-contests, or by awarding prizes to all finalists.
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Papers by Aner Sela