In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures r... more In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium, exists when R > 2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete, and show that full rent dissipation occurs when the strategy space is continuous. Our results are shown to be consistent with recent experimental evidence on the dissipation of rents.
We derive a necessary and sufficient condition for the existence of equilibria with only two acti... more We derive a necessary and sufficient condition for the existence of equilibria with only two active players in the all-pay auction with complete information and identity-dependent externalities. This condition shows that the generic equilibrium of the standard all-pay auction is robust to the introduction of "small" identity-dependent externalities. In general, however, the presence of identity-dependent externalities invalidates well-established qualitative results concerning the set of equilibria of the first-price all-pay auction with complete information. With identity-dependent externalities equilibria are generally not payoff equivalent, and identical players may earn different payoffs in equilibrium. These observations show that Siegel's (2009) results characterizing the set of equilibrium payoffs in all-pay contests, including the all-pay auction as a special case, do not extend to environments with identity-dependent externalities. We further compare the all-pay auction with identity-dependent externalities to the first-price winner-pay auction with identity-dependent externalities. We demonstrate that the equilibrium payoffs of the all-pay auction and winner-pay auction cannot be ranked unambiguously in the presence of identity-dependent externalities by providing examples of environments where equilibrium payoffs in the all-pay auction dominate those in the winner-pay auction and vice versa.
In this note, we characterize the full set of Equilibria of the 2-firm patent race analyzed by Am... more In this note, we characterize the full set of Equilibria of the 2-firm patent race analyzed by Amaldoss and Jain (Management Science, 48(8), August 2002, pp. 972-991). Contrary to Amaldoss and Jain’s (2002) claim, we show that the equilibrium is not always unique and that the set of Equilibria is non-robust to changes in the (discrete) set of available strategies. In some Equilibria, the qualitative results are the reverse of those in the only equilibrium Amaldoss and Jain identify. Our findings have important implications for the analysis of the data from Amaldoss and Jain’s experiments, as well as other experiments appearing in the literature.
Jn this paper, we investigate project selection choices of duopolists facing two alternatives: lu... more Jn this paper, we investigate project selection choices of duopolists facing two alternatives: lundertaking a "pioneering" type project (Type A) aimed to develop a highly innovative product, or an "incremental innovation" type project (Type B) aimed to develop a less innovative product such as the ...
This article examines behavior in the two-player, constant-sum Colonel Blotto game with asymmetri... more This article examines behavior in the two-player, constant-sum Colonel Blotto game with asymmetric resources in which players maximize the expected number of battlefields won. The experimental results support the main qualitative predictions of the theory. In the auction treatment, where winning a battlefield is deterministic, disadvantaged players use a "guerilla warfare" strategy which stochastically allocates zero resources to a subset of battlefields. Advantaged players employ a "stochastic complete coverage" strategy, allocating random, but positive, resource levels across the battlefields. In the lottery treatment, where winning a battlefield is probabilistic, both players divide their resources equally across all battlefields. However, we also find interesting behavioral deviations from the theory and discuss their implications.
This article analyzes a multi-winner contest with players distributed around a ring network. Play... more This article analyzes a multi-winner contest with players distributed around a ring network. Players expend costly effort and a fixed number of adjacent players are selected as the winning coalition by applying a lottery contest success function to the sum of the individual bids of all possible groups of adjacent players. Hence, the players view other players as both friends and foes, and coalitions are formed endogenously. With symmetric valuations, we characterize the unique symmetric equilibrium and compare our results with previous studies of multi-winner contests. We characterize equilibrium for two specific examples under asymmetric valuations. Implications for the role of economic network and contest design issues are explored.
This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In e... more This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In each period firms simultaneously set a price-quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell at this price. Under price-quantity competition firms are able to ration their output below capacity. For a wide range of capacity pairs, the equilibrium path providing the smaller firm with its highest stationary perfect equilibrium payoff requires that it undercut its rival's price and ration demand. Furthermore, for some capacities and discount factors supporting security level punishments, price shading and rationing arise everywhere on the set of stationary perfect equilibrium paths yielding (constrained) Pareto optimal payoffs. That is, price shading may not only be consistent with successful collusion, it may be a requirement of successful collusion. . 2 This commitment to a quantity is made without incurring production costs. Costly production takes place "to order," only after the price-and ceiling-determined sales are realized.
In this note, we characterize the full set of Equilibria of the 2-firm patent race analyzed by Am... more In this note, we characterize the full set of Equilibria of the 2-firm patent race analyzed by Amaldoss and Jain (Management Science, 48(8), August 2002, pp. 972-991). Contrary to Amaldoss and Jain’s (2002) claim, we show that the equilibrium is not always unique and that the set of Equilibria is non-robust to changes in the (discrete) set of available strategies. In some Equilibria, the qualitative results are the reverse of those in the only equilibrium Amaldoss and Jain identify. Our findings have important implications for the analysis of the data from Amaldoss and Jain’s experiments, as well as other experiments appearing in the literature.
This article analyzes tacit collusion in infinitely repeated multiunit uniform price auctions in ... more This article analyzes tacit collusion in infinitely repeated multiunit uniform price auctions in a symmetric oligopolywith capacity-constrained firms.Under two popular definitions of the uniform price, when each firm sets a price-quantity pair, perfect collusion with equal sharing of profit is easier to sustain in the uniform price auction than in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary
This paper examines the feasibility of tacit collusion in price setting duopoly supergames with c... more This paper examines the feasibility of tacit collusion in price setting duopoly supergames with capacity constrained firms. We assume that in each period firms simultaneously set a price-quantity pair specifying the price for the pe- riod and the maximum quantity the firm is willing to sell at this price. Under price-quantity competition firms are able to ration their output below
This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In e... more This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In each period firms simultaneously set a price-quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell as this price. Under price-quantity competition firms are able to ration their output below capacity. For a wide range of capacity pairs, the
In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures r... more In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium, exists when R > 2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete, and show that full rent dissipation occurs when the strategy space is continuous. Our results are shown to be consistent with recent experimental evidence on the dissipation of rents.
We derive a necessary and sufficient condition for the existence of equilibria with only two acti... more We derive a necessary and sufficient condition for the existence of equilibria with only two active players in the all-pay auction with complete information and identity-dependent externalities. This condition shows that the generic equilibrium of the standard all-pay auction is robust to the introduction of "small" identity-dependent externalities. In general, however, the presence of identity-dependent externalities invalidates well-established qualitative results concerning the set of equilibria of the first-price all-pay auction with complete information. With identity-dependent externalities equilibria are generally not payoff equivalent, and identical players may earn different payoffs in equilibrium. These observations show that Siegel's (2009) results characterizing the set of equilibrium payoffs in all-pay contests, including the all-pay auction as a special case, do not extend to environments with identity-dependent externalities. We further compare the all-pay auction with identity-dependent externalities to the first-price winner-pay auction with identity-dependent externalities. We demonstrate that the equilibrium payoffs of the all-pay auction and winner-pay auction cannot be ranked unambiguously in the presence of identity-dependent externalities by providing examples of environments where equilibrium payoffs in the all-pay auction dominate those in the winner-pay auction and vice versa.
In this note, we characterize the full set of Equilibria of the 2-firm patent race analyzed by Am... more In this note, we characterize the full set of Equilibria of the 2-firm patent race analyzed by Amaldoss and Jain (Management Science, 48(8), August 2002, pp. 972-991). Contrary to Amaldoss and Jain’s (2002) claim, we show that the equilibrium is not always unique and that the set of Equilibria is non-robust to changes in the (discrete) set of available strategies. In some Equilibria, the qualitative results are the reverse of those in the only equilibrium Amaldoss and Jain identify. Our findings have important implications for the analysis of the data from Amaldoss and Jain’s experiments, as well as other experiments appearing in the literature.
Jn this paper, we investigate project selection choices of duopolists facing two alternatives: lu... more Jn this paper, we investigate project selection choices of duopolists facing two alternatives: lundertaking a "pioneering" type project (Type A) aimed to develop a highly innovative product, or an "incremental innovation" type project (Type B) aimed to develop a less innovative product such as the ...
This article examines behavior in the two-player, constant-sum Colonel Blotto game with asymmetri... more This article examines behavior in the two-player, constant-sum Colonel Blotto game with asymmetric resources in which players maximize the expected number of battlefields won. The experimental results support the main qualitative predictions of the theory. In the auction treatment, where winning a battlefield is deterministic, disadvantaged players use a "guerilla warfare" strategy which stochastically allocates zero resources to a subset of battlefields. Advantaged players employ a "stochastic complete coverage" strategy, allocating random, but positive, resource levels across the battlefields. In the lottery treatment, where winning a battlefield is probabilistic, both players divide their resources equally across all battlefields. However, we also find interesting behavioral deviations from the theory and discuss their implications.
This article analyzes a multi-winner contest with players distributed around a ring network. Play... more This article analyzes a multi-winner contest with players distributed around a ring network. Players expend costly effort and a fixed number of adjacent players are selected as the winning coalition by applying a lottery contest success function to the sum of the individual bids of all possible groups of adjacent players. Hence, the players view other players as both friends and foes, and coalitions are formed endogenously. With symmetric valuations, we characterize the unique symmetric equilibrium and compare our results with previous studies of multi-winner contests. We characterize equilibrium for two specific examples under asymmetric valuations. Implications for the role of economic network and contest design issues are explored.
This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In e... more This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In each period firms simultaneously set a price-quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell at this price. Under price-quantity competition firms are able to ration their output below capacity. For a wide range of capacity pairs, the equilibrium path providing the smaller firm with its highest stationary perfect equilibrium payoff requires that it undercut its rival's price and ration demand. Furthermore, for some capacities and discount factors supporting security level punishments, price shading and rationing arise everywhere on the set of stationary perfect equilibrium paths yielding (constrained) Pareto optimal payoffs. That is, price shading may not only be consistent with successful collusion, it may be a requirement of successful collusion. . 2 This commitment to a quantity is made without incurring production costs. Costly production takes place "to order," only after the price-and ceiling-determined sales are realized.
In this note, we characterize the full set of Equilibria of the 2-firm patent race analyzed by Am... more In this note, we characterize the full set of Equilibria of the 2-firm patent race analyzed by Amaldoss and Jain (Management Science, 48(8), August 2002, pp. 972-991). Contrary to Amaldoss and Jain’s (2002) claim, we show that the equilibrium is not always unique and that the set of Equilibria is non-robust to changes in the (discrete) set of available strategies. In some Equilibria, the qualitative results are the reverse of those in the only equilibrium Amaldoss and Jain identify. Our findings have important implications for the analysis of the data from Amaldoss and Jain’s experiments, as well as other experiments appearing in the literature.
This article analyzes tacit collusion in infinitely repeated multiunit uniform price auctions in ... more This article analyzes tacit collusion in infinitely repeated multiunit uniform price auctions in a symmetric oligopolywith capacity-constrained firms.Under two popular definitions of the uniform price, when each firm sets a price-quantity pair, perfect collusion with equal sharing of profit is easier to sustain in the uniform price auction than in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary
This paper examines the feasibility of tacit collusion in price setting duopoly supergames with c... more This paper examines the feasibility of tacit collusion in price setting duopoly supergames with capacity constrained firms. We assume that in each period firms simultaneously set a price-quantity pair specifying the price for the pe- riod and the maximum quantity the firm is willing to sell at this price. Under price-quantity competition firms are able to ration their output below
This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In e... more This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In each period firms simultaneously set a price-quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell as this price. Under price-quantity competition firms are able to ration their output below capacity. For a wide range of capacity pairs, the
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Papers by Dan Kovenock