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Infinite multistage games G with games Γ(·) played on each stage are considered. The definition of path and trajectory in graph tree are introduced. For infinite multistage games G a regularization procedure is introduced and in the regularizied game a strong Nash Equilibrium (coalition proof) is constructed. The approach considered in this paper is similar to one used in the proof of Folk theorems for infinitely repeated games. The repeated n-person "Prisoner's Dilemma" game is considered, as a special case. For this game a strong Nash Equilibrium is found.

We analyze the pre- and post-election processes as a two-period game between an incumbent and a challenger. Before the election, in period 1, an incumbent allocates resources into production, fighting with the challenger, and providing public goods, which impact the probability of winning an election. After the election, in period 2 the incumbent may accept the election result, or a coalition or standoff may follow. Six outcomes are that the incumbent wins, the challenger wins, and that a standoff or coalition arises after one of the players wins. We analyze the incumbent’s and challenger’s strategic choices, how these choices depend on a variety of parameters, and the impact of the choices. The analysis is mapped to and tested against empirics of 48 African elections during 2009–2015 which are classified into the six outcomes. To test the model empirically, the correlations between three variables (the incumbent’s fighting and public goods provision and the challenger’s fighting, in period 1) and the six election outcomes are determined for 48 African elections.

Two adversarial actors interact controversially. Early incomplete evidence emerges about which actor is at fault. In period 1 of a two-period game, two media organizations identify ideologically with each of the two actors who are the players exerting manipulation efforts to support the actor they represent. In period 2, the full evidence emerges. Again, the two players exert efforts to support their preferred actor. This paper illustrates the players’ strategic dilemmas for the typical event that actor 1 is considerably at fault based on the early evidence, and much less at fault based on the full evidence. The model assumes that exerting effort in period 1 implies reward or punishment in period 2 depending on whether the full evidence exceeds the early evidence. Twelve parameters in the model are varied individually relative to a benchmark. For example, the players’ efforts are inverse U shaped to an extent in which the actors they identify with are at fault in the two periods. Increasing the evidence ratio intensity causes lower efforts since the players become more unequally matched.