Transitional Dynamics in a Tullock Contest with a General Cost Function

Abstract

This paper constructs and analyzes open-loop equilibria in an infinitely repeated Tullock contest in which two contestants contribute efforts to accumulate individual asset stocks over time.To investigate the transitional dynamics of the contest in the case of a general cost function, we linearize the model around the steady state. Our analysis shows that optimal asset stocks and their speed of convergence to the steady state crucially depend on the elasticity of marginal effort costs, the discount factor and the depreciation rate. In the case of a cost function with a constant elasticity of marginal costs, a lower discount factor, a higher depreciation rate and a lower elasticity imply a higher speed of convergence to the steady state. We further analyze the effects of second prizes in the contest. A higher prize spread increases individual and aggregate asset stocks, but does not alter the balance of the contest in the long run. During the transition, a higher prize spread increases asset stocks, produces a more balanced contest in each period and increases the speed of convergence to the steady state.

The Role of Noise in Alliance Formation and Collusion in Conflicts

“…As in the case of exponential noise, increasing the degree of noise in this CSF also has the effect of discouraging expenditures. Thus, we assume that α ∈ [0, α) where α := (n − 1)v/n 2 so that the stage game's unique Nash equilibrium is interior; if instead α ≥ α, the stage game's unique Nash equi-7 There also exist a number of studies that analyze explicit collusion in one-shot contests (e.g., Leitzel (1991, 1996) and Huck et al (2002)) and that develop models of infinitely repeated contests to analyze non-collusive behavior (e.g., Itaya and Sano (2003), Mehlum and Moene (2006), Krähmer (2007), Eggert et al (2011), and Grossmann et al (2011)). librium has each player making an expenditure of 0 and there exists no form of collusion yielding players a Pareto improvement thus making the analysis of incentives for collusion moot.…”

Tacit Collusion in Repeated Contests with Noise

“…When players attempt to sustain collusion by using Nash reversion strategies, Shaffer and Shogren (2008) show that a decrease in this exponent (i.e., an increase in the level of noise in the contest) makes sustaining collusion more difficult by making the Nash reversion punishment less severe. 4 Shaffer and Shogren (2008) also show 2 There also exist a number of studies that analyze explicit collusion in one-shot contests (Alexeev & Leitzel, 1991, 1996Huck, Konrad, & Müller, 2002) and that develop models of infinitely repeated contests to analyze non-collusive behavior (Itaya & Sano, 2003;Mehlum & Moene, 2006;Krähmer, 2007;Eggert et al, 2011;Grossmann, Lang, & Dietl, 2011).…”