Farsighted Rationality [component]

Karos Dominik, Kasper Laura
2018 unpublished
Farsighted deviations are based on agents' abilities to compare the outcome of a farsighted deviation to the status quo. However, agents do not account for deviations by others in case they do not change the status quo; so, they are not fully farsighted. We use extended expectation functions to capture a coalition's belief about subsequent moves of other coalitions in both cases. We provide three stability and optimality axioms on coalition behavior and show that an expectation function
more » ... on function satisfies these axioms if and only if it corresponds to an equilibrium of the abstract game that is stable with respect to coalitional deviations. We provide applications of our solution for games in characteristic function form and matching problems. An abstract game consists of a set of states (or outcomes), agents' utilities in each state, and an effectivity correspondence that specifies for any two states what coalitions can enforce a move from one to the other. In particular, it does not specify strategies for any player; specifically it abstracts away any strategic interaction. Put differently, abstract games specify what coalitions can achieve, but not how. Both cooperative and non-cooperative games can, therefore, be modeled as abstract games. Naturally, one can use both cooperative and non-cooperative instruments to solve these games. Cooperative solutions of abstract games heavily rely on dominance: one state dominates another state if there is a coalition that (i) can implement a change from the latter to the former, and (ii) thereby achieves a strictly better outcome for all their members. The most prominent solutions based on dominance are, arguably, the stable set (von Neumann and Morgenstern, 1944) and the core (Gillies, 1959) . Both these solutions make the same crucial assumptions about agents' reasoning, namely that agents are myopic: (a) whenever a coalition deviates to a new state, they expect to remain in that state; (b) whenever a coalition does not deviate to a new state, they expect to remain in the old state. That is, coalitions expect that no other coalition will ever implement a change. While assumption (a) has already been weakened in the literature on farsighted behavior, assumption (b) has been criticized (for instance by Chwe, 1994), but a convincing solution has not been offered yet. This paper attempts to do so, both in terms of a dominance relation and in terms of an equilibrium in a non-cooperative game that is stable with respect to coalitional deviations.
doi:10.26481/umagsb.2018011 fatcat:btk23ldr2zftvppu6b77ex6swq