Unscrupulous diner's dilemma
In game theory, the unscrupulous diner's dilemma (or just diner's dilemma) is an n-player prisoner's dilemma. The situation imagined is that several people go out to eat, and before ordering, they agree to split the cost equally between them. Each diner must now choose whether to order the costly or cheap dish. It is presupposed that the costlier dish is better than the cheaper, but not by enough to warrant paying the difference when eating alone. Each diner reasons that, by ordering the costlier dish, the extra cost to their own bill will be small, and thus the better dinner is worth the money. However, all diners having reasoned thus, they each end up paying for the costlier dish, which by assumption, is worse than had they each ordered the cheaper.
Formal definition and equilibrium analysis
Let a represent the joy of eating the expensive meal, b the joy of eating the cheap meal, k is the cost of the expensive meal, l the cost of the cheap meal, and n the number of players. From the description above we have the following ordering . Also, in order to make the game sufficiently similar to the Prisoner's dilemma we presume that one would prefer to order the expensive meal given others will help defray the cost,
Consider an arbitrary set of strategies by a player's opponent. Let the total cost of the other players' meals be x. The cost of ordering the cheap meal is and the cost of ordering the expensive meal is . So the utilities for each meal are for the expensive meal and for the cheaper meal. By assumption, the utility of ordering the expensive meal is higher. Remember that the choice of opponents' strategies was arbitrary and that the situation is symmetric. This proves that the expensive meal is strictly dominant and thus the unique Nash equilibrium.
If everyone orders the expensive meal all of the diners pay k and the utility of every player is . On the other hand, if all the individuals had ordered the cheap meal, the utility of every player would have been . Since by assumption , everyone would be better off. This demonstrates the similarity between the diner's dilemma and the prisoner's dilemma. Like the prisoner's dilemma, everyone is worse off by playing the unique equilibrium than they would have been if they collectively pursued another strategy.[1]
Experimental evidence
Gneezy, Haruvy, and Yafe (2004) tested these results in a field experiment. Groups of six diners faced different billing arrangements. In one arrangement the diners pay individually, in the second they split the bill evenly between themselves and in the third the meal is paid entirely by the experimenter. As predicted, the consumption is the smallest when the payment is individually made, the largest when the meal is free and in-between for the even split. In a fourth arrangement, each participant pays only one sixth of their individual meal and the experimenter pay the rest, to account for possible unselfishness and social considerations. There was no difference between the amount consumed by these groups and those splitting the total cost of the meal equally. As the private cost of increased consumption is the same for both treatments but splitting the cost imposes a burden on other group members, this indicates that participants did not take the welfare of others into account when making their choices. This contrasts to a large number of laboratory experiments where subjects face analytically similar choices but the context is more abstract.[2]
See also
- Tragedy of the commons
- Free-rider problem
- Abilene paradox
References
- ^ Glance, Natalie S.; Huberman, Bernardo A. (March 1994). "The dynamics of social dilemmas". Scientific American.
- ^ Gneezy, Uri; Haruvy, Ernan; Yafe, Hadas (April 2004). "The inefficiency of splitting the bill" (PDF). The Economic Journal. 114 (495): 265–280. doi:10.1111/j.1468-0297.2004.00209.x. Archived (PDF) from the original on 2016-02-05. Retrieved 2015-06-08.
External links
- If You're Paying, I'll Have Top Sirloin by Russell Roberts
- v
- t
- e
- Congestion game
- Cooperative game
- Determinacy
- Escalation of commitment
- Extensive-form game
- First-player and second-player win
- Game complexity
- Graphical game
- Hierarchy of beliefs
- Information set
- Normal-form game
- Preference
- Sequential game
- Simultaneous game
- Simultaneous action selection
- Solved game
- Succinct game
concepts
- Bayes correlated equilibrium
- Bayesian Nash equilibrium
- Berge equilibrium
- Core
- Correlated equilibrium
- Epsilon-equilibrium
- Evolutionarily stable strategy
- Gibbs equilibrium
- Mertens-stable equilibrium
- Markov perfect equilibrium
- Nash equilibrium
- Pareto efficiency
- Perfect Bayesian equilibrium
- Proper equilibrium
- Quantal response equilibrium
- Quasi-perfect equilibrium
- Risk dominance
- Satisfaction equilibrium
- Self-confirming equilibrium
- Sequential equilibrium
- Shapley value
- Strong Nash equilibrium
- Subgame perfection
- Trembling hand
of games
- Go
- Chess
- Infinite chess
- Checkers
- Tic-tac-toe
- Prisoner's dilemma
- Gift-exchange game
- Optional prisoner's dilemma
- Traveler's dilemma
- Coordination game
- Chicken
- Centipede game
- Lewis signaling game
- Volunteer's dilemma
- Dollar auction
- Battle of the sexes
- Stag hunt
- Matching pennies
- Ultimatum game
- Rock paper scissors
- Pirate game
- Dictator game
- Public goods game
- Blotto game
- War of attrition
- El Farol Bar problem
- Fair division
- Fair cake-cutting
- Cournot game
- Deadlock
- Diner's dilemma
- Guess 2/3 of the average
- Kuhn poker
- Nash bargaining game
- Induction puzzles
- Trust game
- Princess and monster game
- Rendezvous problem
figures
- Albert W. Tucker
- Amos Tversky
- Antoine Augustin Cournot
- Ariel Rubinstein
- Claude Shannon
- Daniel Kahneman
- David K. Levine
- David M. Kreps
- Donald B. Gillies
- Drew Fudenberg
- Eric Maskin
- Harold W. Kuhn
- Herbert Simon
- Hervé Moulin
- John Conway
- Jean Tirole
- Jean-François Mertens
- Jennifer Tour Chayes
- John Harsanyi
- John Maynard Smith
- John Nash
- John von Neumann
- Kenneth Arrow
- Kenneth Binmore
- Leonid Hurwicz
- Lloyd Shapley
- Melvin Dresher
- Merrill M. Flood
- Olga Bondareva
- Oskar Morgenstern
- Paul Milgrom
- Peyton Young
- Reinhard Selten
- Robert Axelrod
- Robert Aumann
- Robert B. Wilson
- Roger Myerson
- Samuel Bowles
- Suzanne Scotchmer
- Thomas Schelling
- William Vickrey
- All-pay auction
- Alpha–beta pruning
- Bertrand paradox
- Bounded rationality
- Combinatorial game theory
- Confrontation analysis
- Coopetition
- Evolutionary game theory
- First-move advantage in chess
- Glossary of game theory
- List of game theorists
- List of games in game theory
- No-win situation
- Paradox of tolerance
- Solving chess
- Topological game
- Tragedy of the commons
- Tyranny of small decisions