Best response dynamics with level-n expectations in two-stage games

Dawid H, Heitmann D (2014)
Journal of Economic Dynamics and Control 41: 130-153.

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Journal Article | Published | English
Abstract
This paper analyzes behavior in repeatedly played two-stage games, where players choose actions in both stages according to best replies using 'level-n expectations' about the opponent's actions in both stages. Level-n expectations are recursively de nied in a way that a player holding level n expectations correctly predicts the action of an opponent holding level n-1 expectations. A general conceptual framework to study such dynamics for two-stage games is developed and it is shown that, contrary to results for single-stage games, the fixed points of the dynamics depend on the level of the expectations. In particular, for level-zero expectation, fixed points correspond to a Nash equilibrium of a simultaneous move version of the game, whereas (under certain conditions) fixed points converge towards the subgame perfect equilibrium of the two-stage game if the level of expectations goes to in finity. The approach is illustrated using a two-stage duopoly game, where fi rms in the fi rst stage invest in activities reducing their marginal costs and in the second stage engage in Cournot competition. An increase in the level of expectations leads in the long run to higher cost reducing activities and higher output of the fi rms, however to lower profi ts. Level-two expectations are sufficient to move the fi xed-point of the dynamics to a close neighbourhood of the subgame-perfect equilibrium.
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Dawid H, Heitmann D. Best response dynamics with level-n expectations in two-stage games. Journal of Economic Dynamics and Control. 2014;41:130-153.
Dawid, H., & Heitmann, D. (2014). Best response dynamics with level-n expectations in two-stage games. Journal of Economic Dynamics and Control, 41, 130-153.
Dawid, H., and Heitmann, D. (2014). Best response dynamics with level-n expectations in two-stage games. Journal of Economic Dynamics and Control 41, 130-153.
Dawid, H., & Heitmann, D., 2014. Best response dynamics with level-n expectations in two-stage games. Journal of Economic Dynamics and Control, 41, p 130-153.
H. Dawid and D. Heitmann, “Best response dynamics with level-n expectations in two-stage games”, Journal of Economic Dynamics and Control, vol. 41, 2014, pp. 130-153.
Dawid, H., Heitmann, D.: Best response dynamics with level-n expectations in two-stage games. Journal of Economic Dynamics and Control. 41, 130-153 (2014).
Dawid, Herbert, and Heitmann, Dennis. “Best response dynamics with level-n expectations in two-stage games”. Journal of Economic Dynamics and Control 41 (2014): 130-153.
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