Download PDF by Barmak J.A., Minian E.G.: 2-Dimension from the Topological Viewpoint

By Barmak J.A., Minian E.G.

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1 shows the Prisoner’s Dilemma in strategy space and in payoff space. 1 Since two strategy combinations could yield the same payoffs, we should refer to the inverse correspondence, but for the strict ordinal 2 × 2 games the problem cannot arise. 1 do not completely capture the strategic form. The points U L and DL, for example, are linked in the sense that, by choosing L, the column player limits the outcomes available for the row player to U L or DL. We call the set of payoff vectors when one player’s choices are fixed the inducement correspondence, short for what Greenberg calls the inducement correspondence for the Nash situation.

The points U L and DL, for example, are linked in the sense that, by choosing L, the column player limits the outcomes available for the row player to U L or DL. We call the set of payoff vectors when one player’s choices are fixed the inducement correspondence, short for what Greenberg calls the inducement correspondence for the Nash situation. An inducement correspondence is a general term for a set of positions that one player can bring about, or “induce”. When we refer to “Row’s inducement correspondence” we mean the set of outcomes induced by the column player for the row player to choose from.

E. removing a swap) removes edges from the graph6 . With one important and recurring exception, restricting the set of operators partitions the 2 × 2 games into a set of identical subspaces with identical graphs7 . Among the games in each of these subspaces, payoffs vary in a simple and restricted way. Topological features can be deduced from either the group structure or from the graph structure. We generally work from the graph or subgraph, but at each stage we describe the associated groups.

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2-Dimension from the Topological Viewpoint by Barmak J.A., Minian E.G.


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