What Is the Traveler’s Dilemma?
The traveler’s dilemma, in game theory, is a non-zero-sum recreation by which two gamers try to maximise their very own payoff, with out regard for the opposite. The sport demonstrates the “paradox of rationality“—the irony that making selections illogically or naively usually produces a greater payoff in recreation principle.
- The Traveler’s dilemma is a recreation the place two gamers every bid on a proposed payoff and each obtain the decrease bid, plus or minus a bonus payoff.
- In response to recreation principle, the rational technique for each gamers is to decide on the bottom potential payoff which ends up in each gamers receiving decrease payoffs than they may obtain by following an irrational technique.
- In experimental research, folks persistently selected increased payoffs and achieved higher outcomes than the rational technique predicted by recreation principle.
Understanding the Traveler’s Dilemma
The traveler’s dilemma recreation, formulated in 1994 by economist Kaushik Basu, presents a state of affairs by which an airline severely damages equivalent antiques bought by two completely different vacationers. Administration is prepared to compensate them for the lack of the antiques, however since they do not know about their worth, they inform the 2 vacationers to individually write down their estimate of the worth as any quantity between $2 and $100 with out conferring with each other.
Nevertheless, there are a few caveats:
- If each vacationers write down the identical quantity, they are going to be reimbursed that quantity.
- In the event that they write completely different numbers, administration will assume that the cheaper price is the precise worth and that the particular person with the upper quantity is dishonest. Whereas they’ll pay each of them the decrease determine, the particular person with the decrease quantity will get a $2 bonus for honesty, whereas the one who wrote the upper quantity will get a $2 penalty.
The rational selection, when it comes to the Nash equilibrium, is $2. The reasoning goes as follows.
- Traveler A’s first impulse could also be to jot down down $100 and if Traveler B additionally writes down $100, that’s the quantity each will obtain from the airline administration.
- However, if Traveler A places down $99 and if Traveler B places down $100, then A would obtain $101 ($99 + $2 bonus).
- However A believes that this line of considering can even happen to B, and if B additionally places down $99, each would obtain $99. So A would actually be higher off placing down $98, and receiving $100 ($98 + $2 bonus) if B writes $99.
- However since this similar considered writing $98 might happen to B, A considers placing down $97, and so forth.
- This line of backward induction will take the vacationers all the way in which right down to the smallest permissible quantity, which is $2.
Selecting Nash Equilibrium
In experimental research, opposite to the predictions of recreation principle, most individuals decide $100 or a quantity near it, both with out considering the issue by means of or whereas totally conscious they’re deviating from the rational selection. So, whereas most individuals intuitively really feel that they would choose a a lot increased quantity than $2, this instinct appears to contradict the logical consequence predicted by recreation principle—that every traveler would choose $2. By rejecting the logical selection and performing illogically by writing a better quantity, folks find yourself getting a considerably larger payoff.
These outcomes agree with related research utilizing different video games such because the Prisoner’s Dilemma and the Public Goods recreation, the place experimental topics have a tendency not to decide on the Nash equilibrium. Based mostly on these research, researchers have proposed that folks seem to have a pure, optimistic perspective in favor of cooperation. This perspective results in cooperative equilibria that present increased payoffs to all gamers in single-shot or repeated video games and could be defined by selective evolutionary pressures that favor these sorts of seemingly irrational however useful methods.
Nevertheless, traveler’s dilemma research have additionally proven that when the penalty/bonus is bigger or when the gamers include groups of a number of individuals who make a standard choice, then the gamers extra usually select to observe the rational technique that results in the Nash equilibrium. These results additionally work together, in that groups of gamers not solely select the extra rational technique however are additionally much more conscious of the scale of the penalty/bonus than particular person gamers.
These research recommend that developed methods that are inclined to create useful social outcomes could be offset by extra rational methods that have a tendency towards the Nash equilibrium relying on the construction of the incentives and the presence of social divisions.