Strategic Interactions: Analytical and Behavioral Game Theory

Game theory analyzes the play of two or more players who have their strategies and are influenced by each other’s actions. In other words, game theory examines situations in which decision-makers can make the most strategic and profitable decisions against others. Therefore, the gain of the individual or group in the event of competition depends on the decisions of other individuals and groups participating in this competitive environment. In short, game theory is a mathematical discipline that investigates the competition and cooperation between decision-makers.

The main elements in a game can be listed as follows: • Players: They are the decision-makers in a game. • Actions: These are the options offered to the players. • Outcomes: Results like a price war that occurs at the end of the game. • Strategies: Plans that take into account all possibilities of how other players will act. • Payoffs: Losses or gains that players make at the end of the game. • Information: It is the knowledge that the players have in the decision-making process. • Equilibrium: It is a stable result that may not always be the best outcome.

Games differ from each other in terms of their characteristics. The playing styles and applied strategies of the games may differ. Games can be classified as follows: Number of players, Information Set, Payoffs, (Non)cooperative behavior, Periods,

Dominant strategy is a strategy that maximizes a player’s payoff regardless of the actions of other players.

Nash equilibrium is each player’s best response to the strategies of the others.

Information set is the knowledge that a player has when it is his turn to move.

A sequential equilibrium gives each player the probability distributions for the strategies in each information set. In other words, the sequential equilibrium starts out by having a probability distribution about which of the information sets is more reasonable. Players choose the strategies with the highest payoff in each information set, taking into account their probability distribution. Thus, the strategy profiles of the players provide a consistent and optimal choice according to the probability distributions in each information set.

Camerer (2009) states that the purpose of behavioral game theory is to predict how individuals, firms, and other collective entities behave. Accordingly, four main elements bring analytical game theory closer to behavioral game theory: Representation, initial conditions, learning, and social preferences over outcomes.

Gintis (2005) discussed behavioral economics theory in 5 mostly interconnected and overlapping stages: i. The first began with the paradoxes advanced by Ellsberg and Allais in the early 1950s and 1960s. According to them, the expected benefit is nonlinear. ii. The second is the study of Vernon Smith et al. (1956). They began conducting laboratory experiments on economic markets at their universities. iii. The third started with Amos Tversky, Daniel Kahneman, and their other colleagues in the early 1970s. They created models of decision-making outside of the standard model, such as expectancy theory, regret theory, and hyperbolic reduction. iv. The fourth includes games such as bargaining, trust, and public goods games that have been performed by many different researchers [Guth et al. (1982), Roth et al. (1991), Berg et al. (1995)] since the 1980s. Thus, strategic interaction conditions were incorporated into the decision-making process. v. The fifth includes various experimental scenarios performed by Ernst Fehr and some other researchers since the early 2000s. These researchers built extended models by incorporating strategic interactions into rational decision theory.

Experiments used in behavioral game theory have revealed that the observed outcomes of games are different from the perspective of analytical game theory. Van Damme (2015) remarks on some empirical findings of the experiments as follows:

• Framing effects are a considerable determinant of the outcome of games.

• The outcomes of games can consist of sides of analytical game theory that it assumes to be unreasonable.

• Players’ strategies do not always have to be the best strategy. Minor differences in payoffs are negligible.

• Players care not only about their payoff but also other things.

• The results of one-stage games may not always be unbounded rational.

• Players sometimes may not use the backward induction method, but it can be learned.

• As players play the games, they get experience and modify their behavior. However, this process can be quite slow.

The ultimatum game is a simple bargaining game on how a certain sum of money will be split between two players. One of the players in the game is called the proposer (or allocator), and the other is called the responder (or recipient). The proposer is given some money and is asked to share it with the responder whom he does not know or see. In other words, both players are unaware of who the other is. If the responder accepts this offer, both players will receive the money within the current offer. However, the responder can refuse this offer, in which case neither player will earn the money. The analytical game theory argues that it is the best strategy for the proposer to offer the smallest positive value they can offer and for the responder to accept that offer. Because, a homo-economicus should make the lowest offer to another person whom he has never met, and another homo-economicus should accept this complimentary offer from a person he does not know at all. In this way, they can maximize their utilities. According to analytical game theory, this is the subgame perfect Nash equilibrium. However, this does not always happen. In many studies on the subject, findings claiming the opposite had been reached.

Altruism is the opposite of selfish behavior. It means looking after the interests of others as well as your own.

Reciprocity refers to the way individuals act to benefit (or harm) other individuals who benefit (or harm) them, by responding in the same way.

The Ultimatum Game is a bargaining game in which Player 1 is the proposer and Player 2 is the responder. In the dictator game, another bargaining game, the responder feature of Player 2 is removed. This means: As in the ultimatum game, Player 1 (dictator) offers Player 2 a part of the amount given to him. However, Player 2 no longer has a chance to respond. He has to get his share. (The Dictator game differs from previous games in this respect. Player 2 has no function either. However, it is customarily defined as a game and the second individual is Player 2.) Player 1 can give some or all of his money to an unknown Player 2. The game ends with this decision of Player 1. According to analytical game theory, the subgame perfect Nash equilibrium occurs when Player 1 takes all the money for himself. Because that’s what a homoeconomicus does.

Inequality aversion refers to the resistance of individuals to injustice and inequality results

Moral hazard is when one party to a contract harms another by changing behavior to the detriment of the other. The moral hazard here is the worker’s low effort by abusing the high salary paid by the fair and well-intentioned employer.

Free rider problem is the idea that the consumption of public goods can be continued without incurring any cost, arising from the characteristics of public goods such as non-rivalness and non-excludability.

"Limited strategic thinking" means that individuals are relatively lacking in mental and thinking processes while trying to reach any goal.

Mixed-Strategy Equilibrium Games are games where players mix their strategy with probability distributions rather than a specific strategy.  In such games, one player chooses a certain strategy, while the other player wins if he guesses the strategy chosen by the first player. Therefore, the right thing for players is to act unpredictably. However, although these games are assumed to be initially randomized, they are not randomized when played repeatedly. As individuals attempt to randomize their choices, they exhibit some cognitive biases.

Signaling is the action of transmitting information from one player to another.