Hang Ren, Tingliang Huang, in Computers & Operations Research, 2018, The concept of Nash equilibrium requires the common knowledge of rationality, i.e., each player makes rational choices, knows that other players make rational choices, and knows that other players know that she makes rational choices, etc. 3. For an example, consider the game 1 1 The authors suggest to introduce a centralized virtual referee whose role is to prevent users with high co-channel interference from sharing one subcarrier, or to reduce the demanded transmission rates that prove to be unfeasible. We refer interested readers to Camereretal. The smart insider chooses not to launch attack. This statement must be interpreted carefully. I realize that the terminology here has a kind of S&M flavor to it, with all this talk of 'strict domination' and the like. Otherwise, if p(A+1)+1<1, an attacker attacks with probability. I get there because if you suppose the column player mixes in general (playing L with probability q), then $5q + 3(1-q) = q + 2(1-q) \Rightarrow q = \frac{-1}{3}$ which is impossible and so the column player doesn't mix. To understand the impact of the defender's preference parameter D to an insider Ai's strategy, we first consider the case where Ai knows the exact value of D. 0000035896 00000 n In Fig. In your case, the unique Nash eq is in pure strategies. When b > 0, it is extremely difficult to derive an analytical expression of the Nash equilibrium for a generic false positive function l (as in Theorem 1). 0000027185 00000 n 0000025912 00000 n L is the number of information bits per frame, M is the total number of bits in a frame, R expresses the bit rate, Pi is the transmission power of each link and f(SI(N)Ri) is a function that approximates the probability of correct reception of a frame. 0000036489 00000 n Nash Equilibrium is a term used in game theory to describe an equilibrium where each player's strategy is optimal given the strategies of all other players. Nash Equilibrium is a game theory Game Theory Game theory is a mathematical framework developed to address problems with conflicting or cooperating parties who are able to make rational decisions.The concept that determines the optimal solution in a non-cooperative game in which each player lacks any incentive to change his/her initial strategy. 0000034415 00000 n Nonetheless, once the reputation satisfies rD(i)1(A+1) and forces Ai to abstain, the defender's reputation from the view of Ai+1 will remain the same as rD(i) because no attack has taken place to change it. In the noncooperative game, the focus is on whether a, Modeling customer bounded rationality in operations management: A review and research opportunities, Camerer, 2003; Camerer etal., 2004; Nagel, 1995; Stahl and Wilson, 1994, A survey on resource allocation techniques in OFDM(A) networks, , Wu et al. Given a point a* and a function, f:A , the upper-level set for a* is given by U(a*) = {a A:f(a) a*}. MathJax reference. Proof. 0000034773 00000 n Intuitively, this means that if any given player were told the strategies of all their opponents, they still would choose to retain their original strategy. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players and no player has anything to gain by changing only their own strategy. Figure 15.11. The unique pure strategy Nash equilibrium is T,C, which gives the payos2,1. The process is repeated until the prices converge to the Nash equilibrium (line 7). They also provided sufficient conditions for the existence of a Nash equilibrium in the cases of n=3 and n=4. The change from Fig. 0000036415 00000 n In other words, it is preferable for a link to achieve a lower SI(N)R, as the value of its utility function will be higher. There may be more than one Nash equilibrium, so we can't always talk about 'the' Nash equilibrium. The third result establishes the support of the Nash solution in an n-person bargaining game by the unique subgame perfect
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