Behavioral game theory

Behavioral game theory analyzes interactive strategic decisions and behavior using the methods of game theory,[1] experimental economics, and experimental psychology. Experiments include testing deviations from typical simplifications of economic theory such as the independence axiom[2] and neglect of altruism,[3] fairness,[4] and framing effects.[5] As a research program, the subject is a development of the last three decades.[6]

Traditional game theory focuses on the mathematical structure of equilibria, and tends to use basic rational choice involving utility maximization. In contrast, behavioral game theory focuses on how actual behavior tends to deviate from standard predictions: how can we explain and model those deviations, and how can we make better predictions using more accurate models?[7] Choices studied in behavioral game theory are not always rational and do not always represent the utility maximizing choice.[8]

Behavioral game theory uses laboratory and field experiments, as well as modeling – both theoretical and computational.[8] Recently, methods from machine learning have been applied in work at the intersection of economics, psychology, and computer science to improve both prediction and understanding of behavior in games.[9][10]

History

Behavioral game theory began with the work of Allais in 1953 and Ellsberg in 1961. They discovered the Allais paradox and the Ellsberg paradox, respectively.[7] Both paradoxes show that choices made by participants in a game do not reflect the benefit they expect to receive from making those choices. In the 1970s the work of Vernon Smith showed that economic markets could be examined experimentally rather than only theoretically.[7] At the same time, several economists conducted experiments that discovered variations of traditional decision-making models such as regret theory, prospect theory, and hyperbolic discounting.[7] These discoveries showed that actual decision makers consider many factors when making choices. For example, a person may seek to minimize the amount of regret they will feel after making a decision and weigh their options based on the amount of regret they anticipate from each. Because they were not previously examined by traditional economic theory, factors such as regret along with many others fueled further research.

1980년대부터 실험자들은 합리적인 선택으로부터 차이를 일으키는 조건들을 조사하기 시작했다. 최후통첩과 흥정 게임은 감정이 상대 행동 예측에 미치는 영향을 조사했다. 최후통첩 게임의 가장 잘 알려진 예로는 '은행가'가 준 금전적 최후통첩에 근거해 참가자가 판매하거나 경기를 계속하는 결정을 내려야 하는 텔레비전 쇼 '딜'이나 '노딜'이 있다. 이러한 게임들은 또한 신뢰가 의사결정 결과와 행동을 최대화하는 효용성에 미치는 영향을 탐구했다.[11] 공통 자원 게임은 협력과 사회적 만족도가 피험자의 선택에 어떻게 영향을 미치는지 실험적으로 시험하기 위해 사용되었다. 일반적인 자원 게임의 실제 예는 음식 접시에서 가져갈 파티 손님의 결정일 수 있다. 손님들의 결정은 그들이 얼마나 배고픈지에 의해서만 영향을 받을 뿐만 아니라, 공유 자원인 음식이 얼마나 남았는지, 그리고 다른 사람들이 그들이 더 많이 먹는 것에 대해 판단할 것이라고 믿는 경우에 영향을 받을 것이다. 이 기간 동안 실험자들은 효용을 극대화하지 못한 행동을 참가자의 결함 있는 추론의 결과로 간주하였다.[7] 세기가 바뀔 무렵 경제학자들과 심리학자들이 이 연구를 확대했다. 합리적인 선택 이론에 근거한 모델들은 의사결정자의 선호도를 반영하고 효용을 극대화하지 못한 선택을 합리화하려고 시도하도록 수정되었다.[7]

전통 게임 이론과 비교

전통적인 게임 이론은 이론적 모델을 사용하여 게임 내 모든 플레이어들의 가장 유익한 선택을 결정한다.[12] 게임 이론은 효용 극대화 결정을 예측하기 위해 플레이어의 상식에 대한 가정과 함께 합리적인 선택 이론을 사용한다.[12] 그것은 또한 선수들이 상대의 전략을 예측할 수 있게 해준다.[13] 전통적인 게임 이론은 이성적인 참가자들이 선택해야 할 결정을 정확히 지적하려고 하지만 왜 그러한 결정이 내려졌는지 설명하려고 하지 않기 때문에 주로 규범적인 이론이다.[13] 합리성은 게임 이론의 일차적 가정이기 때문에, 다른 형태의 이성적 결정이나 불합리한 결정에 대한 설명은 없다.[13]

행동 게임 이론은 규범적인 이론이라기보다는 주로 긍정적인 이론이다.[13] 양성 이론은 정확한 작용을 규정하기보다는 현상을 기술하려고 한다. 긍정적인 이론은 시험할 수 있어야 하며 진실 또는 거짓으로 증명될 수 있다. 규범적 이론은 주관적이고 의견을 바탕으로 한다. 이 때문에 규범적 이론은 진실이나 거짓으로 증명될 수 없다. 행동 게임 이론은 실험 데이터를 사용하여 의사 결정을 설명하려고 시도한다.[13] 이 이론은 둘 다 실제 실험을 통해 조사되기 때문에 합리적이고 비합리적인 결정을 허용한다. 구체적으로, 행동 게임 이론은 실제 세계의 결정에 영향을 미치는 요소들을 설명하려고 시도한다.[13] 이러한 요인들은 전통적인 게임 이론의 영역에서 탐구되지 않고, 경험적 데이터를 사용하여 가정하고 관찰할 수 있다.[13] 행동 게임 이론에서 나온 발견들은 더 높은 외부 타당성을 갖는 경향이 있을 것이고 실제 세계의 의사결정 행동에 더 잘 적용될 수 있을 것이다.[13]

행동 게임 이론 연구에 사용된 게임의 예

참고 항목: 게임 이론의 게임 목록

게임의 합리성에 영향을 미치는 요인

믿음

의사결정 게임에서 다른 사람들에 대한 믿음이 이성적인 선택을 하는 능력에 영향을 미칠 것으로 예상된다. 그러나 다른 사람들의 믿음은 또한 실험 결과를 평형, 효용 극대화 결정에서 벗어나게 할 수 있다. 코스타고메즈(2008)의 실험에서 참가자들은 다른 참가자들과 함께 일련의 정상적인 형태의 게임을 완성하기 전에 상대방의 행동에 대한 그들의 첫 번째 순서 믿음에 대해 질문을 받았다.[17] 참가자들은 오직 35%의 시간을 준수했다. 또한 참가자들은 상대가 전통적 게임 이론 평형을 15% 준수할 것이라는 믿음만 진술했다.[17] 이것은 참가자들이 상대편이 실제보다 덜 이성적일 것이라고 믿었다는 것을 의미한다. 이 연구의 결과는 참여자들이 효용 최대화 조치를 선택하지 않고 반대자들도 그렇게 하기를 기대한다는 것을 보여준다.[17] 또한, 그 결과는 참가자들이 상대방의 행동에 대한 그들의 신념에 부합하는 효용 극대화 행동을 선택하지 않았다는 것을 보여준다.[17] 참가자들은 상대가 어떤 결정을 내릴 가능성이 더 높다고 믿었을지 모르지만, 마치 상대가 무작위로 선택하는 것처럼 여전히 결정을 내렸다.[17] TV 프로그램 '딜' 또는 '노딜'의 참가자들을 조사한 또 다른 연구는 이성적 선택과는 차이를 발견했다.[18] 참가자들은 게임을 진행할 때 이전 결과에 근거하여 결정을 내릴 가능성이 더 높았다.[18] 경기 내에서 참가자들의 기대를 충족시키지 못했을 때 위험 회피는 줄어들었다. 예를 들어 일련의 긍정적인 결과를 경험한 주체는 거래를 받아들이고 게임을 끝낼 가능성이 낮았다. 경기 초반 주로 부정적인 결과를 경험한 과목도 마찬가지였다.[18]

Social cooperation

Social behavior and cooperation with other participants are two factors that are not modeled in traditional game theory, but are often seen in an experimental setting. The evolution of social norms has been neglected in decision-making models, but these norms influence the ways in which real people interact with one another and make choices.[11] One tendency is for a person to be a strong reciprocator.[11] This type of person enters a game with the predisposition to cooperate with other players. They will increase their cooperation levels in response to cooperation from other players and decrease their cooperation levels, even at their own expense, to punish players who do not cooperate.[11] This is not payoff-maximizing behavior, as a strong reciprocator is willing to reduce their payoff in order to encourage cooperation from others.

Dufwenberg and Kirchsteiger (2004) developed a model based on reciprocity called the sequential reciprocity equilibrium. This model adapts traditional game theory logic to the idea that players reciprocate actions in order to cooperate.[19] The model had been used to more accurately predict experimental outcomes of classic games such as the prisoner's dilemma and the centipede game. Rabin (1993) also created a fairness equilibrium that measures altruism's effect on choices.[20] He found that when a player is altruistic to another player the second player is more likely to reciprocate that altruism.[20] This is due to the idea of fairness.[20] Fairness equilibriums take the form of mutual maximum, where both players choose an outcome that benefits both of them the most, or mutual minimum, where both players choose an outcome that hurts both of them the most.[20] These equilibriums are also Nash equilibriums, but they incorporate the willingness of participants to cooperate and play fair.

Incentives, consequences, and deception

The role of incentives and consequences in decision-making is interesting to behavioral game theorists because it affects rational behavior. Post (2008) analyzed Deal or no Deal contestant behavior in order to reach conclusions about decision-making when stakes are high.[18] Studying the contestant's choices formed the conclusion that in a sequential game with high stakes decisions were based on previous outcomes rather than rationality.[18] Players who face a succession of good outcomes, in this case they eliminate the low-value cases from play, or players who face a succession of poor outcomes become less risk averse.[18] This means that players who are having exceptionally good or exceptionally bad outcomes are more likely to gamble and continue playing than average players. The lucky or unlucky players were willing to reject offers of over one hundred percent of the expected value of their case in order to continue playing.[18] This shows a shift from risk avoiding behavior to risk seeking behavior. This study highlights behavioral biases that are not accounted for by traditional game theory. Riskier behavior in unlucky contestants can be attributed to the break-even effect, which states that gamblers will continue to make risky decisions in order to win back money.[18] On the other hand, riskier behavior in lucky contestants can be explained by the house-money effect, which states that winning gamblers are more likely to make risky decisions because they perceive that they are not gambling with their own money.[18] This analysis shows that incentives influence rational choice, especially when players make a series of decisions.

Incentives and consequences also play a large role in deception in games. Gneezy (2005) studied deception using a cheap talk sender-receiver game.[21] In this type of game player one receives information about the payouts of option A and option B. Then, player one gives a recommendation to player two about which option to take. Player one can choose to deceive player two, and player two can choose to reject player one's advice. Gneezy found that participants were more sensitive to their gain from lying than to their opponent's loss.[21] He also found that participants were not wholly selfish and cared about how much their opponents lost from their deception, but this effect diminished as their own payout increased.[21] These findings show that decision makers examine both incentives to lie and consequences of lying in order to decide whether or not to lie. In general people are averse to lying, but given the right incentives they tend to ignore consequences.[21] Wang (2009) also used a cheap talk game to study deception in participants with an incentive to deceive.[22] Using eye tracking he found that participants who received information about payoffs focused on their own payoff twice as often as their opponents.[22] This suggests minimal strategic thinking. Further, participants' pupils dilated when they sent a deceiving, and they dilated more when telling a bigger lie.[22] Through these physical cues Wang concluded that deception is cognitively difficult.[22] These findings show that factors such as incentives, consequences, and deception can create irrational decisions and affect the way games unfold.

Group decisions

Behavioral game theory considers the effects of groups on rationality. In the real world many decisions are made by teams, yet traditional game theory uses an individual as a decision maker. This created a need to model group decision-making behavior. Bornstein and Yaniv (1998) examined the difference in rationality between groups and individuals in an ultimatum game.[23] In this game player one (or group one) decides what percentage of a payout to give to player two (or group two) and then player two decides whether to accept or reject this offer. Participants in the group condition were put in groups of three and allowed to deliberate on their decisions.[23] Perfect rationality in this game would be player one offering player two none of the payout, but that is almost never the case in observed offers. Bornstein and Yaniv found that groups were less generous, willing to give up a smaller portion of the payoff, in the player one condition and more accepting of low offers in the player two condition than individuals.[23] These results suggest that groups are more rational than individuals.[23]

Kocher and Sutter (2005) used a beauty contest game to study and compare individual and group behavior.[24] A beauty contest game is one where all participants choose a number between zero and one hundred. The winner is the participant who chooses a number closest to two thirds of the average number. In the first round the rational choice would be thirty-three, as it is two thirds of the average number, fifty. Given an infinite number of rounds all participants should choose zero according to game theory. Kocher and Sutter found that groups did not perform more rationally than individuals in the first round of the game.[24] However, groups performed more rationally than individuals in subsequent rounds.[24] This shows that groups are able to learn the game and adapt their strategy faster than individuals.

See also

References

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