A direct sum form is proposed for constructing a composite game from two 2 x 2 games, prisoner's dilemma and snowdrift game. This kind of direct sum form game is called a multiple roles game. The replicator dynamics of the multiple roles game with will-mixed populations is explored. The dynamical behaviors on square lattice are investigated by numerical simulation. It is found that the dynamica...

We develop a general framework for inverse optimal control that distinguishes between rationalizing demonstrated behavior and imitating inductively inferred behavior. This enables learning for more general imitative evaluation measures and differences between the capabilities of the demonstrator and those of the learner (i.e., differences in embodiment). Our formulation takes the form of a zero...

many studies have been conducted to determine the efficiency of two-stage network structures in the recent years. the two-stage network with additional inputs to the second stage, in which the second stage is independent of the first stage are one of these structures. thus, there is a need for a model capable of calculating the efficiency of two-stage structures as well as efficiency of each st...

In this lecture we will discuss 2-player zero sum games. Such games are completely competitive , where whatever one player wins, the other must lose. Examples of such games include chess, checkers, backgammon, etc. We will show that in such games: • An equilibrium always exists; • All equilibrium points yield the same payoff for all players; • The set of equilibrium points is actually the carte...

صلاخلا ـ ة : ُّ دعتُ ل ثم ةيعيبطلا تاغللا ةجلاعم تاقيبطت نم ديدعلل ايساسأ انوكم ةيعوضوملا ةئزجتلا قيبطت تامولعملا عاجرتساو صوصنلا صيخلت . نم فدهلا وه ثحبلا اذ ه قت و مي ةيعوضوملا ة ئزجتلا تا يمزراوخ ة يلاعف ضوملا دودحلا ى لع فرعتلا يف ة يبرعلا صوصنلا لخاد ةيعو . م تو قايس لا اذ ه يف ة فلتخم رداصم نم ةيبرع صوصن ةسمخ لخاد اهنوظحلاي يتلا ةركفلا وأ عوضوملا تاريغت ىلع فرعتلل ةيبرعلا ةغللا ءارق نم ة...

We have seen that Nash equilibria in two-player zero-sum games (and generalizations thereof) are polynomial-time tractable from a centralized computation perspective. We have also seen that the payoff matrix of a zero-sum game determines a unique value for the row player and a unique value for the column player (summing to zero), which specify their payoffs in all equilibria of the game. In thi...

Matching Pennies is a well-known example of a two player, zero-sum game. In this game, each of the players, the matcher and the mismatcher, flips a coin, and the payoffs are determined as follows. If the coins come up matching (i.e., both heads or both tails), then the matcher wins, so the mismatcher pays the matcher the sum of $1. If the coins do not match (i.e., one head and one tail), then t...

The additive attack public mutual information game is explicitly solved for one of the simplest quantization based watermarking schemes, the scalar Costa scheme (SCS). It is a zero-sum game played between the embedder and the attacker, and the payoff function is the mutual information. The solution of the game, a subgame perfect nash equilibrium, is found by backward induction. Therefore, the B...