Dynamic multilevel game theory

The dissertation develops dynamic multilevel (hierarchical) game theory. I embrace, generalize, and expand upon conventional game theory, acknowledging methodological individualism, individual rationality, incentive compatibility, sequential rationality, while incorporating the notion of multilevel organization. Phenomena typically occur at multiple levels of organization, with generally strong between-level and between-actor linkages. A formal apparatus is developed for representing multilevel phenomena game-theoretically. A hierarchy A is formalized, with an arbitrary number of levels, and an arbitrary number of actors at each level. Each actor has a certain strategy set that is exhaustively described, and receives a payoff given the combinations of strategies chosen by the actor itself and all the other actors in the hierarchy. Interdependencies of strategy sets and payoff sets for the various actors and levels are specified. A rigorous method is developed where strategy sets are determined by working upwards in the hierarchy, and payoffs and equilibria are determined by working downwards in the hierarchy. This suggests a solution to theoretical dilemmas concerning the connection of micro- and macro-level analysis. The time-factor is introduced, allowing for determination of strategy sets (1) without accounting for the outcome of games played earlier in time, (2) accounting for the accumulation of outcomes of games played earlier in time at lower levels, (3) at lower and the same levels, (4) and at lower, the same, and higher levels. Analytical methods and simulation techniques are employed complementarily. Collective rent seeking is analyzed with an evolutionary mechanism allowing for intergroup migration and intergroup warfare. Division of labor within each of multiple groups engaged in collective rent seeking is scrutinized, applying the Folk theorem to show the conditions under which leadership struggle gets intensified or alleviated. Prior models have ignored the fact that groups exist in a context of other groups with which they, through individual agents within the groups, interact or compete. Some of these models have thereby made simplifications that generate unfortunate biases in the results, which are demonstrated. The dissertation investigates the effects of considering more realistic models by accounting for the presence of multiplicities of groups and groups embedded in hierarchies.