Reputation (game theory)

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The term reputation is used in game theory to describe the effect that a player's actions in the course of the game have on his or her credibility (game theory) in the eyes of the opponent and the behavior of the players in the future. With the game-theoretic approach, fundamental statements about reputation (“reputation”) as a social factor can be obtained.

Importance in game theory

Each player embodies a certain type of player during a game . The strategic behavior of every type of player can be explained with the help of reputation. How important a player's reputation is to a player depends on whether the game is unique or whether it is played multiple times. In addition, reputation gains in importance when incomplete information is available.

Repeated games

Building a reputation and the associated credibility of the player are all the more important the more games are played. It can be one and the same or another opponent. The player wants to convince the opponent during the repeated games that his strategic move is credible. It is also in his interest to build a positive reputation in order to create trust. This creates a self-bond through which the player is no longer able to break his promise. The previous doubts of the opponents can be overcome, whereby the credibility of the strategic move can be established.

Building a negative reputation can also open up the possibility of self-commitment. The aim is to destroy the reputation and the once-built credibility of keeping promises. This makes it clear to the opponent that in future no games will be played that do not serve the player's own interests.

In addition to the strategic motives for a reputation that have already been shown, there are also non-strategic reasons that can lead to credibility.

Incomplete information

In games with incomplete information , the level of information of the players is different. This means that one, several or all players do not know all the payouts or preferences of the other players. In addition, if a player has information that is reserved only for him, and this is known to the other players, they will use his behavior as a guide and adjust their further action steps accordingly in order to reveal the hidden information.

The reputation of the player therefore arises from his behavior, which the opponents can observe. In contrast to repeated games, games with incomplete information offer the possibility of successfully influencing the expectations and thus the actions of the opponents through bluffs or deception.

application

Building a Positive Reputation - Credibility of a Promise

A company expands and uses the reputation of previous products. The company promises its customers to manufacture the new products in the same quality as the old products. The company's self-commitment does not make it possible for it to break its promise , because then its reputation and credibility would decline. The company will accordingly stick to what it has promised its customers so that the positive reputation can be maintained or expanded.

Building a negative reputation - the credibility of a threat

In principle, a government decides to prevent future threats by threatening never to submit to them. In the event of a hostage-taking, this means that the government never threatens to negotiate with the hostage-takers. However, the kidnappers will assume that once the hostages are in their hands, it will not be possible for the government not to negotiate. Against this background, the government is negotiating with the hostage-takers and thereby destroying the credibility of their promises. After the destruction of the credibility and the consequent destruction of the reputation, the government sees no need to hold on to self-commitment and attacks the kidnappers after the negotiated solution. Although the government has ruined the credibility of its promises, it is making the threat of never negotiating credible again.

Credibility of a non-strategic reason

The feeling of pride is meant to represent this non-strategic reason. It is conceivable that the pride of belonging to a community leads to the fact that one behaves accordingly in the community due to the already existing reputation.

Incomplete information

In a game of cards, each player receives 3 cards that only he can look at. Then he announces his decision about the mission. The cards are placed face up on the table and the highest hand wins. This card game is a game with incomplete information. The players do not know what the other players have for cards and try to infer the hand through their facial expressions and gestures in order to make their own decision dependent on it.

Game theory examples

Whether a player behaves according to his reputation depends on the benefit he can derive from his reputation. This means that the player will behave according to his reputation as long as his benefits are greater than the costs of his behavior.

Repeated games

Employer A is looking for new workers B. Due to his previous dealings with his workers, A has built up a good reputation. He can maintain this until he begins to exploit his workers . If A exploits his workers, he builds a bad reputation. B will only start work with A if A has a good reputation. As a result, A would only exploit his potential worker B if he has built a bad reputation. If A is known to have never exploited any of his workers in the past, then B will work for A too. On the other hand, if A has previously exploited every one of his workers, B can expect that he too will be exploited if he works for A. Thus, B will reject the job offer.

However, the relationship between employer and employee should be based on trust. The employer is dependent on his employees in order to be able to process orders. As a result, his good reputation will be worth more to him than a short-term gain that would result from the exploitation. As long as A can maintain his reputation, he gets a payout of 1 every round of the game (assuming a number of rounds of 10, this means a payout of 10). If the employer were to exploit his workers, he would get a payout of 2 per round. After the first round, however, the workers would no longer want to work for A. Although A receives a higher profit in the first round, he would not receive any further payouts in the following rounds because no worker would be willing to allow himself to be further exploited. So the result after 10 rounds is 10> 2. This shows that it is better for employers to maintain or expand their reputation.

Incomplete information

There are two types of players 1. On the one hand, the "ordinary" player (O) and on the other hand the " cooperative " player (C). Compared to the "ordinary" player, the "cooperative" player is much more unselfish. This means that he likes to share and invest , regardless of whether the other player does the same. The probability that a player is type O is ¾ and ¼ that he is a cooperative type C player. Player 1 knows whether he is a "cooperative" or "common" guy. However, player 2 does not know this about player 1. Thus, there is a case of incomplete information.

The illustrated game trees should be the basis for the example.

Reputation (game theory)

If it can be assumed that player 1 definitely wants to invest and always makes benevolent decisions, regardless of what player 2 does, player 1 will choose B '. If player 1 is rather selfish and only concerned with his advantage, his optimal decision is S, because that is where he receives the largest payout.

In addition, in a game with incomplete information, it must be considered how high the individual information of the player is. Player 2 will only choose I if its benefits are greater than its costs , otherwise he will be undecided whether to choose I or N.

If player 2 has been able to collect information about player 1 and if player 1 decides type O for N and type C for I ', then player 2 can determine on the basis of the information available that player 1 is type C. Because of this, player 2 will definitely choose I.

However, if player 1 assumes that player 2 is investing, player 1 will also invest type O, although he initially pursued a different strategy. On the other hand, player 2 cannot find out anything about player 1 type O if he chooses to invest and he has not found out enough information about player 1 by then.

If Player 2 watches Player 1 invest, Player 2 is more likely to be a cooperative type of player. By investing, the “ordinary” player (O) gives the impression that he is a cooperative type. Thus, the existence of a cooperative gamer type helps the common gamer to build a reputation for cooperative behavior.

literature

supporting documents

  1. ↑ See Joel Watson: Strategy - An Introduction to Game Theory, p. 211.
  2. ↑ See Sabrina Helm: Corporate Reputation and Stakeholder Loyalty, p. 111.
  3. ↑ See Avinash K. Dixit , Barry J. Nalebuff: Game Theory for Beginners, p. 142.
  4. ↑ See Sabrina Helm: Company Reputation and Stakeholder Loyalty, p. 110.
  5. ↑ Cf. Avinash K. Dixit , Barry J. Nalebuff: Game theory for beginners, p. 142 ff.
  6. ↑ See Alfred Wagenhofer / Ralf Ewert: External corporate accounting, p. 44.
  7. ↑ See Paul Terres: The logic of a competitive monetary order, p. 224.
  8. ↑ See Sabrina Helm: Corporate Reputation and Stakeholder Loyalty, p. 111.
  9. ↑ Cf. Christian Ullrich: The dynamics of Coopetition, p. 166.
  10. ↑ See Avinash K. Dixit , Susan Skeath: Games of Strategy, p. 334.
  11. ^ Based on Avinash K. Dixit , Barry J. Nalebuff: Game theory for beginners, p. 143 f.
  12. ↑ See Avinash K. Dixit , Barry J. Nalebuff: Game Theory for Beginners, p. 143.
  13. ↑ See Alfred Wagenhofer / Ralf Ewert: External corporate accounting, p. 44.
  14. ↑ See Sabrina Helm: Company Reputation and Stakeholder Loyalty, p. 110.
  15. ↑ See David M. Kreps : Game Theory and Economic Modeling. P. 67 ff.
  16. ↑ See Joel Watson: Strategy - An Introduction to Game Theory, pp. 286 ff.