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12 Chapter 2. Nash Equilibrium: Theory A very wide range of situations may be modeled as strategic games. For exam-ple, the players may be rms, the actions prices, and the preferences a reection of the rms’ prots. Or the players may be candidates for political ofce, the actions
The best way to understand the importance of Nash’s contributions is by comparing the state of game theory just after publication of von Neumann and Morgenstern’s book in 1944 with its state after publication of Nash’s four papers in 1953.
This resource contains information regarding nash equilibrium.
BR2(p 1) 2 [p + "; 1) So this cannot be a Nash equilibrium. Case 4: p1 = c. BR2(p1) = (c; +1) p1 = c. BR2(p1) = (c; +1) The unique pure strategy Nash equilibrium is p1 = p2 = c Thus in contrast to the Cournot duopoly model, in the Bertrand competition model, two = c) rms get us back to perfect competition.
In 1950, John Nash contributed a remarkable one-page PNAS article that defined and characterized a notion of equilibrium for n-person games. This notion, now called the ‘‘Nash equilibrium,’’ has been widely applied and adapted in economics and other behav-ioral sciences.
In 1994, The Nobel Prize in Economics was awarded to the game theorist John Nash, who, in the early 1950s, formulated elegant mathematical models for the strategic interaction among small numbers of decision-makers in situations involving elements of both conflict and cooperation.
Nash Equilibrium: The Rationalistic Interpretation. A non-cooperative game is given by a set of players, each having a set of strategies and a payoff function. A strategy vector is a Nash equilibrium if each player's strategy maximizes his payoff if the strategies of the others are held fixed.
