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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.

We consider the bin packing problem with cardinality constraints in a non-cooperative game setting. In the game, there are a set of items with sizes between 0 and 1, and a number of bins each of which has a capacity of 1. Each bin can pack at most $k$ items, for a given integer parameter $k\ge 2$. The social cost is the number of bins used in the packing. Each item tries to be packed into one of the bins so as to minimize its cost. The selfish behaviors of the items result in some kind of equilibrium, which greatly depends on the cost rule in the game. We say a cost rule encourages sharing if for an item, compared with sharing a bin with some other items, staying in a bin alone does not decrease its cost. In this paper, we first show that for any bin packing game with cardinality constraints under an encourage-sharing cost rule, the price of anarchy of it is at least $2-\frac{2}{k}$. We then propose a cost rule and show that the price of anarchy of the bin packing game under the rule is $2-\frac{2}{k}$ when $k\ge 7$.

A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell's Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob's assumption is wrongThis is formalized to show that any belief model of a certain kind must have a “hole.” An interpretation of the result is that if the analyst's tools are available to the players in a game, then there are statements that the players can think about but cannot assume. Connections are made to some questions in the foundations of game theory.