|
Special case: a "strong" cooperative player receives Uk Kk, n-1 symmetric "weak" players’ get u k whereby
|
tarix | 08.12.2017 | ölçüsü | 485 b. | | #14732 |
|
Heterogeneity of costs and gains: Ui, Ki for i = 1, …, N; Ui > (Ui – Ki) > 0 Special case: A “strong” cooperative player receives Uk – Kk , N-1 symmetric “weak” players’ get U – K whereby: Uk – Kk > U – K Strategy profile of an “asymmetric”, efficient (Pareto optimal) Nash equilibrium: s = (Ck, D, D, D, D, …,D) i.e. the “strong player” is the volunteer (the player with the lowest cost and/or the highest gain). All other players defect. ► In the asymmetric dilemma: Exploitation of the strong player by the weak actors. ►Paradox of mixed Nash equilibrium: The strongest player has the smallest likelihood to take action!
Asymmetric VOD. There are two types of Nash-equilibria in an asymmetric VOD. The mixed Nash-equilibrium and the asymmetric pure strategy equilibrium. We expect the asymmetric equilibrium to emerge in an asymmetric game. In our special version, we expect a higher probability of the “strong” player to take action, i.e. to cooperate than “weak” players. (Exploitation of the “strong” by the “weak”)
Group size (symmetric game, experiment III, not presented): Group size (symmetric game, experiment III, not presented): - Complexity of coordination. The efficient provision of the public good decreases with group size.
Learning: - Evolution of norms. The efficient provision of public good and successfull coordination is increasing with the number of repetitions of the game.
Player‘s strength: - Exploitation of strong players. In the asymmetric VOD, the public good was provided to a much higher degree by the strong player compared to weak players (although the probability of efficient public good provision was not larger than for the symmetric VOD).
- Strong player‘s higher likelihood of action is expected by the Harsanyi/Selten theory of equilibrium selection.
Solution of a „Volunteer‘s Dilemma“ by Emperor Penguins
Choose the probability of defection q such that an actor is indifferent concerning the outcome of strategy C and D Choose the probability of defection q such that an actor is indifferent concerning the outcome of strategy C and D U – K = U (1 – qN-1) U – K = U - U qN-1 qN-1 = K/U Defection ► q = N-1√ K/U Cooperation ► p = 1 - N-1√ K/U
H1 Repeated symmetric VOD. There are N asymmetric Nash-equilibria in a stage game. Actors take turn to volunteer (C). The outcome is “efficient” (Pareto optimal) and actors achieve an equal payoff distribution with payoff U – K/N per player. H1 Repeated symmetric VOD. There are N asymmetric Nash-equilibria in a stage game. Actors take turn to volunteer (C). The outcome is “efficient” (Pareto optimal) and actors achieve an equal payoff distribution with payoff U – K/N per player. a) We expect a coordination rule to emerge over time (social learning) b) Coordination is more problematic in larger groups. H2 Asymmetric VOD. There are two types of Nash-equilibria in an asymmetric VOD. The mixed Nash-equilibrium and the asymmetric pure strategy equilibrium. a) We expect the asymmetric equilibrium to emerge in an asymmetric game. In our special version, we expect a higher probability of the “strong” player to take action, i.e. to cooperate than “weak” players. (Exploitation of the “strong” by the “weak”) b) A focal point should help to solve the coordination problem and the focal player is expected to develop a higher intensity of volunteering.
Dostları ilə paylaş: |
|
|