# Human behaviour in one-shot perfect information games

### Background

A one-shot game is one where two participants have some set of actions $$\{1, ... , n\}$$, they make their decision on which option to take (without knowing the decision of their partner, or in sequence depending on game). Based on the action $$i$$ of the first player and $$j$$ of the second player, they receive some reward (or punishment) $$G(i,j)$$. The participants never play again, and are made aware of this before the interaction happens. There is no communication allowed between the participants except making their action choice.

The game is perfect information if the participants are made aware of all possible outcomes of the game ahead of time (they are shown and explained the payoff matrix $$G$$ at least implicitly). The final result depends solely on the mutual decision of the players. From the perspective of the participant, there is no hidden state or chance apart in the action of the opponent.

### Question

Game theory makes predictions on how rational players will behave in such settings. The fun part of psychology is that humans often don't follow these predictions. They cooperate more than they should in Prisoner's dillema (PD), violate the sure-thing principle in turn-based PD (Shafir & Tversky, 1992), reject unfair offers in ultimatum game (Guth et al., 1982), vary across cultures in their propensity to punish in public goods games (Herrmann, et al. 2008), and many other things that game theory doesn't predict.

The experimental literature is vast and divided between anthropology, economics, psychology, and law (just sampling from my own library). Is there a reliable current or canonical survey/summary/meta-analysis of well-controlled laboratory based experiments of human behaviour in one-shot perfect information games?

### Notes

• I prefer artificial well-controlled experiments with a large number of participants over natural or in-the-field experiments.

• The previous point means that I am alright with data just from WEIRD participants, even for games where cultural variation is known to be significant. However, discussions of known cross-cultural effects is welcome.

• Bonus if the summary looks at many different games in very similar experimental setting, and shows games where there is both agreement and disagreement from game-theoretic predictions.

• I am not interested in papers about a single experiments, unless you want to provide a detailed survey of many such papers, their results, and methodology in your answer.

### References

Guth, W., Schmittberger, R., & Schwarze, B. (1982) An experimental analysis of ultimatum bargaining. Journal of Economic Behavior & Organization 3(4): 367-388.

Herrmann, B., Thoni, C., & Gachter, S. (2008) Antisocial punishment across societies. Science 319(5868): 1362-1367.

Shafir, E., & Tversky, A. (1992). Thinking through uncertainty: Nonconsequential reasoning and choice. Cognitive Psychology 24:449-474.

• What's your question? The biggest problem with the participants in game theory is the lack of trust that's created by unequal positions. For participants to go through with their role/play, there must be trust among the players or there's more to lose than the situation they're in now. Too often ppl assume that a participant in a game isn't participating in other games simultaneously. That's where predicting outcome relies heavily on intel. – Den Activist Jun 1 '18 at 5:59
• I do not think a well-controlled laboratory experiment was ever deemed necessary. The level of abstraction game theory implies makes laboratory social or sociological experiments futile if at all possible. The best route of testing this are real-life experiments made by companies who applied these theories and are financially successful, like, most probably, Amazon for example. Now, finding out which concepts and calculations were applied where is something else. Some may guess based on data available, but they will definitely not make the answers available without compensation. My two cents. – OMan Jun 1 '18 at 11:46
• Thank you for the feedback @OMan, I am not asking about game theory in general, but in particular about surveys on one-shot perfect-information games. These are not particularly relevant to Amazon or corporations. Studies on one-shot perfect information games definitely exist, as I am aware of a number of them and reference a few in the question itself. What I am looking for is if there is a single survey or meta-analysis that has brought all (or much) of this work together (since it is distributed over many fields and thus difficult to track on your own). – Artem Kaznatcheev Jun 1 '18 at 21:14

The question seems to ask for reviews; well, a Google Scholar search on...

one-shot + game + review

...yields:

...among a host of other hits (65k+), so enough out there!

The Hagen & Hammerstein (2006) provides a critical review that seems to be matching your 'bonus' question (you're going to upvote my answer twice? :-)

References
- Alessina, American Econom Rev (1988); 78(4): 796-805
- Archettia & Scheuring, J Theor Biol (2012); 299 (2012); 9-20
- Hagen & Hammerstein, Theor Pop Biol (2006); 69(3): 339-48
- Nagarajan & Sošić, Eur J Operat Res (2008); 187(3): 719-45