Basic Game of Trust. Alternative Versions. Prisoner’s Dilemma

Basic Game of Trust. The original 'game of trust' has been described in [Berg1995] as an abstracted investment game. The game is played in pairs and rules of the game are known to both players. Alice, the first player (known also as a buyer or principal) is endowed with $10 and may invest a certain amount of money in Bob who is another player (seller, agent). Bob has also been endowed with $10 but he also receives from the 'bank' three times the amount invested by Alice. He has the opportunity to transfer all or some of his money to Alice (but may decide not to transfer anything).

It has been observed that if both players follow their economic best interests, Alice should never invest and Bob will never be able to re-pay anything, so that both of them ends up gaining $10 each. Monetary flow, its volume and character are attributable entirely to the existence of trust (as there is no control instrument available). Under optimum conditions to trust, Alice should invest all her money in Bob, and he should return her $20, keeping another $20 for himself. The amount of money invested by Alice can be used as a measure of her trust while the amount of money returned by Bob on top of Alice's investment is a measure of his trustworthiness.

Interestingly, what is commonly observed challenges purely selfish justifications. Even under the cloak of anonymity (i.e. where there is no expectation of further interactions), buyers invested in the average $5.16 and sellers returned $4.66 [Berg1995]. The payoff in indefinitely repetitive, non-anonymous games (where the reciprocity can be expected as the relationship develops) is generally higher, even though results vary depending on details of the arrangement.

Note that the payoff in definite repetitive games can be theoretically very similar to non-repetitive games as players can iteratively deduce their preferred strategy from the fact that the other party is likely to default in the last step (see e.g. [Ullmann-Margalit2001]), a testimony to the strength of the continuity factor in trust building.

Alternative Versions. Rules of the game can be reversed into what can be called a game of distrust [Bohnet2005]. In such game, Alice initially has nothing and Bob has $40. Alice may withdraw money from Bob (up to $30) but she will receive only one-third of it (the 'bank' will hold the rest). In the next step Bob can return any of his remaining money to Alice, and this time Alice will receive all this money. Again, if Alice does not trust Bob then her best move is to withdraw $30 (of which she will receive $10) and leave Bob with remaining $10. However, if she withdraws nothing (trusting Bob) then Bob can return her $20 and still keep $20 for himself.

Signalling in the game of trust combines the act of speech and transactional exchange, unlike in real life where the communication usually precedes and facilitates the action. [Ariau2006] proposes an additional declaratory step in the game of trust with incomplete information (i.e. the payoff matrix is not known) to allow both parties to determine the extent of commitment between players. This should allow them to learn to trust each other across repetitions of the game and eventually facilitate the convergence of both players to Pareto-optimal Nash equilibrium.

Changing the initial distribution of endowments (and associated rules) alters the perception and behaviour of players. Assuming that two basic strategies: the economically rational one (no trust) and the optimal one (full trust) should end here in the same financial result, altering the perception causes Alice to trust (invest) twice as much and receive about a half of what she has received in a trust game, as Bob behaves in a less trustworthy manner.

Prisoner’s Dilemma. Other interesting games are e.g. binary-choice trust games [Camerer1988], the gift-exchange game [Fehr1993] and various other forms of social games. Specifically the Prisoner's Dilemma (formalised by W. Tucker in [Poundstone1992]) is popularly used to link trust with economic utility and demonstrate the rationality behind reciprocity.

The Prisoner's Dilemma is defined as a game between two prisoners (hence the name of the game) where each prisoner must make in isolation an independent decision whether he will cooperate or betray (defect) the other one. The payoff function is set in such a way that each prisoner always gains certain benefit if he defects, may gain higher benefit if both prisoners cooperate but may incur significant losses if he cooperates and the other chooses to defect. Rational approach should lead both players to defect so that the decision to cooperate is interpreted as a sign of trust.

The average level of trust can be determined by playing the game in random pairs within the large group. Playing the game repetitively between the same pair allows development of the relationship between participants, specifically if combined with the ability to punish those participants who did not cooperate (which brings elements of control into the scope of the game). Several strategies have been created for players to develop the relationship towards cooperation. Specifically, the strategy of 'tit-for-tat with forgiveness' [O'Riordan2001] allows the quick development of a relationship but permits recovery from incidental crisis, that may be caused e.g. by communication noise or misunderstanding.

Multi-player Games. Regarding games with several participants, trade-based games are very popular. Different forms of close market simulations allow participants to exchange goods for money. For example [Bolton2003], the game may require a buyer to initiate the transaction by sending money to a seller. The seller then can either complete the transaction by shipping goods or default (and keep the money). Such a game also can distinguish between trust (that can be measured as a number of initiated transactions), trustworthiness (a number of transactions completed) and efficiency (the percentage of transactions completed as a fraction of all possible transactions).

If the game is combined with the reputation mechanism (introducing control in addition to trust), it allows for a group-level view on the behaviour of its participants. Buyers can provide feedback to the reputation system and can use the reputation to influence their purchase decisions. Higher reputation usually leads to higher profit so that it is either the final profit or the reputation scoring that can be used as a measure of confidence. Such games can actually be played in a real environment (e.g. [Resnick2006]) leading to interesting findings.

Simulated market-like games may suffer from the same symptoms as the real market sometimes does: facing the prospect of limited continuity, participants may build a reputation only to benefit from destroying it in the last move (e.g. [Bolton2003]).