THE PSYCHOLOGY OF STRATEGY IN GAMES
Due to its unrealistic assumptions about human cognitive ability (perfectly accurate forecasting, for example) and its heavy reliance on equilibrium analysis to predict behavior in social interactions, game theory has not been used by psychologists. However, recent developments in behavioral game theory address these limitations by acknowledging that people's forecasting abilities are limited, allowing for bounded and heterogeneous thinking, and maintaining models that are as broadly applicable as those that use equilibrium analysis. One such psychological approach is cognitive hierarchy (CH) modeling, in which players reason accurately only about those who think less. CH predicts non-equilibrium behaviors that have been observed in more than 100 laboratory experiments and several field settings.
Introduction
A formal method called "game theory" has shown benefits in the fields of political science, economics, and even computer science, sociology, and biology. However, due to its strong presumptions about human behavior, it has not gained much momentum in cognitive and social psychology. These constraints are addressed by recent developments, which we will discuss in this paper together with one significant development in the understanding of sociality and strategic thinking.
Mathematically, social interactions where the decisions made by one player affect the actions of another are described by game theory. The players, their plans, the knowledge they have, the sequence in which they make their decisions, and the value they assign to each result comprise a description of a game or strategic engagement. Results include tangibles (cash won from a game of poker or experiment winnings) and intangibles (emotional satisfaction from enforcing norms or being ahead of others).
The majority of game theorists used equilibrium analysis to forecast tactics up to the 1990s. When players maximize their utility and accurately predict the actions of others, they are said to be in equilibrium. In the game of rock, paper, scissors, for instance, constantly playing "rock" is not an equilibrium tactic. Play "rock" only if you believe your opponent will play "scissors." If they believe you are going to play "rock," they will play "paper," not "scissors." Therefore, playing each hand at random for one-third of the time is the equilibrium approach.
Since theory and evidence point to the possibility that equilibration is the result of adaptive learning and evolutionary selection, an equilibrium can be a valuable predictor of the future state of a social system. But due to cognitive constraints, it is psychologically implausible for people to derive equilibrium strategies purely from thinking. Therefore, equilibrium analysis poorly predicts outcomes when players encounter new games or there is a shift such as a policy or technology change.
In the mid-1990s, game theory was extended to include behavioral models of strategic thinking, called cognitive hierarchy (CH) or level-k models. We focus on CH models, which have been applied to more than 100 experimental games and field settings, and whose process implications have been tested with eye-tracking and data from functional magnetic resonance imaging. This shift centralizes psychology, making cognitive representations of game structures, strategy categorization, and cross-game learning researchable questions, unlike in standard game theory.
What Are The Components Of A Game?
Game theory states that the following elements must exist for a game to exist:
Players: A player makes strategic decisions related to the game. For something to be deemed a game, it must involve two or more players. The game theory would not hold true if there was just one participant. It is also necessary for the players to be able to communicate with one another.
Methodology: The decisions that players make during a game based on potential outcomes are known as strategies.
A player's own self-interest and the actions of the other players are frequently the basis of strategy.
OTHER ELEMENTS OF A GAME
In a game, players share ‘common’ knowledge of the rules, strategies available to them, and the possible payoffs of the game. There is often a ‘information set,’ which is the information available at any given point in the game.
This term is usually applicable when the game has a sequential component
Equilibrium, is the point in the game where the players have made their decisions and an outcome has been reached, states where the game ends.
The fundamental tenets of a game are that players are presumed to behave sensibly and in their own best interests.
Different Game Theory Types
The Dilemma of the Prisoner
Among the most well-known applications of game theory is this particular game. The game has numerous variations, however the following is one of the scenarios:
- Two offenders are apprehended together for a joint offense; they are taken to the police station and questioned separately, preventing them from speaking to each other during the process.
- The inmates are informed that they will each serve five years in prison if they confess to the crime. Should neither admit guilt, they will each be sentenced to two years in prison. But in the event that one prisoner confesses while the other does not, the confessing prisoner will serve three years in jail while the non-confessing prisoner will get nine years.
The problem with this scenario is that each prisoner's reward depends on how the others behave. If they could reach a consensus, they might consent to not confess in exchange for a reduced prison term.
Still, it's impossible to predict what the other person will do. Confession is the safest course of action to prevent the worst-case situation of nine years.
The Game of Ultimatum
This is a straightforward two-player negotiation game. Take it or leave it. The proposer and responder roles are assigned to two players, respectively.
The proposer receives a certain amount of money, say $4. Afterwards, they have to choose how much of the $4 to give the respondent. The decision to accept or reject the offer rests with the respondent.
The proposer suggests that the participants divide the money equally if the respondent accepts. In the event that the offer is turned down, neither participant receives any money.
A low offer from a proposer who acts in self-interest runs the risk of being rejected by the respondent, leaving them both without anything.
Some, however, advise the respondent to take any offer—even if it is only $1—because it is still a gain even in the small amount.
This game makes the assumption that all participants are reasonable, even if there are actually a lot of variables that could affect a person's choice.
The Centipede Game
In this long-form game, two players can take turns taking a bigger portion of a pot of money that is steadily growing. The arrangement is such that a player earns less money than they would have if they had accepted the pot if they give the money pot to another player and then take it themselves.
When one player chooses to take the money pot, they will receive the greater share while the other will receive the smaller portion. This concludes the game. The game has 100 rounds in total, although it can finish before or after the first round.
The Volunteer's Conundrum
In the volunteer's dilemma, an activity or task needs to be completed by someone for the benefit of everybody. Usually, this is a somewhat unpleasant chore that nobody really wants to do but everyone apparently has the ability to finish.
In the worst situation, nobody in the group benefits and the task remains unfinished. Chores like tidying up, fixing a damaged item, or finishing a collaborative project are a few examples of tasks. It is up to each group member to choose whether or not to take the lead and finish the work.
There is no genuine incentive to act because everyone else benefits as long as the volunteer does not receive any additional rewards for performing the assignment.
Types Of Game Strategy
According to game theory, players might employ the following game strategies:
Maximax tactics
When the player tries to get the biggest payout possible, they employ a maximax approach. Even in situations where a very negative result is probable, the player who employs this technique will choose to take a gamble in hopes of attaining the greatest possible result.
Regardless of what the other player choose, the player employing the maximax approach in the Prisoner's Dilemma would select the option with the least prison sentence.
Since this strategy implies a highly advantageous environment for the player, which may not always be the case, it is sometimes seen as naive and unduly optimistic.
Maximin tactics
When using a maximin approach, a player selects the best payout out of all possible options. This is frequently selected when one player cannot completely depend on the other players to adhere to any previous understanding. The worst punishment for confessing in the Prisoner's Dilemma is five years (assuming the other player also confesses), and the worst punishment for denying is nine years (assuming the other player also confesses).
Confession is, therefore, the maximin strategy—the best of the worst outcome.
Prevailing tactics
Regardless of what the other players choose to do, the dominating strategy is what will benefit the player the most. The most common approach in the Prisoner's Dilemma game would be for every player to confess. However, while the dominant strategy may be great in the case of non-alternative if someone is part of a game with more dominant strategies (e.g., each player has a dominant strategy), then this approach will not be optimal.
Conclusions
Models in which people do levels of strategic thinking are a tidy, cognitively-plausible way to understand limits on thinking and provide measurement tools and codification on how treatments and differences influence strategic thinking. This essay shows a mathematical way to model hierarchical levels of thinking, explaining behavior in a number of experimental and field settings. Furthermore, thinking steps can be empirically associated with patterns of visual fixation on information and neural.
