above, the mixing probability of a player should depend only on the other player's payoff, not his own payoff. This deviation can be explained as a quantal response equilibrium. In a quantal-response-equilibrium, the best-response curves are not sharp as in a standard Nash equilibrium. Rather, they change smoothly from the action whose probability is 0 to the action whose probability 1 (in other words, while in a Nash-equilibrium, a player chooses the best response with probability 1 and the worst response with probability 0, in a quantal-response-equilibrium the player chooses the best response with high probability that is smaller than 1 and the worst response with smaller probability that is higher than 0). The equilibrium point is the intersection point of the smoothed curves of the two players, which is different from the Nash-equilibrium point. The own-payoff effects are mitigated by risk aversion. Players tend to underestimate high gains and overestimate high losses; this moves the quantal-response curves and changes the quantal-response-equilibrium point. This apparently contradicts theoretical results regarding the irrelevance of risk-aversion in finitely-repeated zero-sum games. Real-life data The conclusions of laboratory experiments have been criticized on several grounds. Games in lab experiments are artificial and simplistic and do not mimic real-life behavior. The payoffs in lab experiments are small, so subjects do not have much incentive to play optimally. In real life, the market may punish such irrationality and cause players to behave more rationally. Subjects have other considerations besides maximizing monetary payoffs, such as to avoid looking foolish or to please the experimenter. Lab experiments are short and subjects do not have sufficient time to learn the optimal strategy. To overcome these difficulties, several authors have done statistical analyses of professional sports games. These are zero-sum games with very high payoffs, and the players have devoted their lives to become experts. Often such games are strategically similar to matching pennies: In soccer penalty kicks, the kicker has two optionskick left or kick rightand the goalie has two optionsjump left or jump right. The kicker's probability of scoring a goal is higher when the choices do not match, and lower when the choices match. In general, the payoffs are asymmetric because each kicker has a stronger leg (usually the right leg) and his chances are better when kicking to the opposite direction (left). In a close examination of the actions of kickers and goalies, it was found that