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 ====== Games ====== ====== Games ======
 +
 +
 +==== Braess's paradox ====
 +
 +Braess's paradox, credited to the mathematician Dietrich Braess, states that **adding extra capacity to a network when the moving entities selfishly choose their route, can in some cases reduce overall performance**. This is because the Nash equilibrium of such a system is not necessarily optimal.
 +The paradox is stated as follows: "For each point of a road network, let there be given the number of cars starting from it, and the destination of the cars. Under these conditions one wishes to estimate the distribution of traffic flow. Whether one street is preferable to another depends not only on the quality of the road, but also on the density of the flow. If every driver takes the path that looks most favorable to him, the resultant running times need not be minimal. Furthermore, it is indicated by an example that an extension of the road network may cause a redistribution of the traffic that results in longer individual running times."
  
 ====Schelling point==== ====Schelling point====
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 ====Game Theory: Dominance, Nash Equilibrium, Symmetry==== ====Game Theory: Dominance, Nash Equilibrium, Symmetry====
-|B. L. Slantchev, 2007| [[http://www.leg.ufpr.br/~pedro/slantchev-game-theory.pdf|pdf]]|+|B. L. Slantchev, 2007| {{http://www.leg.ufpr.br/~pedro/slantchev-game-theory.pdf|pdf}}|
  
 That is, we must be able to assume not only that all players are rational, but also That is, we must be able to assume not only that all players are rational, but also
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   - **Pure Strategies in a Perturbed Game:** Harsanyi introduced another interpretation of mixed  strategies, according to which a game is a frequently occurring situation, in which players’ preferences are subject to small random perturbations. Like in the previous section, random factors are introduced, but here they affect the payoffs. Each player observes his own preferences but not that of other players. The mixed strategy equilibrium is a summary of the frequencies with which the players choose their actions over time. Establishing this result requires knowledge of Bayesian Games, which we shall obtain later in the course. Harsanyi’s result is so elegant because even if no player makes any effort to use his pure strategies with the required probabilities, the random variations in the payoff functions induce each player to choose the pure strategies with the right frequencies. The equilibrium behavior of other players is such that a player who chooses the uniquely optimal pure strategy for each realization of his payoff function chooses his actions with the frequencies required by his equilibrium mixed strategy.   - **Pure Strategies in a Perturbed Game:** Harsanyi introduced another interpretation of mixed  strategies, according to which a game is a frequently occurring situation, in which players’ preferences are subject to small random perturbations. Like in the previous section, random factors are introduced, but here they affect the payoffs. Each player observes his own preferences but not that of other players. The mixed strategy equilibrium is a summary of the frequencies with which the players choose their actions over time. Establishing this result requires knowledge of Bayesian Games, which we shall obtain later in the course. Harsanyi’s result is so elegant because even if no player makes any effort to use his pure strategies with the required probabilities, the random variations in the payoff functions induce each player to choose the pure strategies with the right frequencies. The equilibrium behavior of other players is such that a player who chooses the uniquely optimal pure strategy for each realization of his payoff function chooses his actions with the frequencies required by his equilibrium mixed strategy.
   - **Beliefs:** Other authors prefer to interpret mixed strategies as beliefs. That is, **the mixed strategy profile is a profile of beliefs, in which each player’s mixed strategy is the common belief of all other players about this player’s strategies**. Here, each player chooses a single strategy, not a mixed one. An equilibrium is a steady state of beliefs, not actions. This interpretation is the one we used when we defined MSNE in terms of best responses. The problem here is that each player chooses an action that is a best response to equilibrium beliefs. The set of these best responses includes every strategy in the support of the equilibrium mixed strategy (a problem similar to the one in the first interpretation).   - **Beliefs:** Other authors prefer to interpret mixed strategies as beliefs. That is, **the mixed strategy profile is a profile of beliefs, in which each player’s mixed strategy is the common belief of all other players about this player’s strategies**. Here, each player chooses a single strategy, not a mixed one. An equilibrium is a steady state of beliefs, not actions. This interpretation is the one we used when we defined MSNE in terms of best responses. The problem here is that each player chooses an action that is a best response to equilibrium beliefs. The set of these best responses includes every strategy in the support of the equilibrium mixed strategy (a problem similar to the one in the first interpretation).
 +
 +
 +====The Economics of Fair Play====
 +|K. Sigmund and E. Fehr and M. A. Nowak, 2002| Scientific American|
 +
 +one round ultimatum game. game of the "sharing" pool with and without punishment. homo economicus and homo emoticus
 +
 +If, for instance, the proposer is chosen not by a flip of a coin but
 +by better performance on a quiz, then offers are routinely a bit lower and get
 +accepted more easily — the inequality is felt to be justified.
 +
 +our emotional apparatus has been shaped by millions of years of living in small groups, where
 +it is hard to keep secrets. Our emotions are thus not finely tuned to interactions
 +occurring under strict anonymity. We expect that our friends, colleagues and
 +neighbors will notice our decisions. If others know that I am content
 +with a small share, they are likely to make me low offers.
 +
 +Because one-shot interactions were rare during human evolution, these emotions
 +do not discriminate between one-shot and repeated interactions.
 +
 +
 +====The Power of Memes====
 +|S. Blackmore, 2000|
 +
 +ver URGENTE: colocar na apresentacao para o referata:
 +"an evolution of ideas, or memes"
  
  
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 Associated with these resources is an NxN payoff matrix M = (M(i, j)). The game is played in N stages and each player is allowed to use each resource once and only once during these N stages. Associated with these resources is an NxN payoff matrix M = (M(i, j)). The game is played in N stages and each player is allowed to use each resource once and only once during these N stages.
- 
  
geopro/pedro/games.1209003101.txt.gz · Última modificação: 2008/04/24 02:11 por pedro