Computing the cores of strategic games with punishment–dominance relations

In this paper, we discuss the computational complexity of the strategic cores of a class of n-person games defined by Masuzawa (Int J Game Theory 32:479–483, 2003), which includes economic situations with monotone externality. We propose an algorithm for finding an α-core strategy of any game in this class which, counting the evaluation of a payoff for a strategy profile as one step, terminates after O(n3· M) operations, where M is the maximum size of a strategy set of any of the n players. The idea underlying this method is based on the property of reduced games.