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Game Theory in Neuroeconomics

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Neuroeconomics

Abstract

Game theory and contemporary decision theory provide the mathematical foundation of economics. Neuroeconomics, which principally concerns itself with the integrative study of brain, mind and behavior, builds on this mathematical foundation while also drawing heavily from the repository of experimental paradigms that have grown out of economic game theory and behavioral economics. Game theory is central to neuroeconomics primarily because it constitutes a formal mathematical framework with which to bridge insights occurring at different levels of neuroeconomic analysis. In particular, game theoretic principles can be used to express neuroscientific ideas about the brain, psychological concepts regarding the human mind, and economic predictions of human behavior, thereby making these different ideas more rigorously relatable to each other. In this chapter we provide a nontechnical introduction to game theory and its relation to neuroeconomics. It has been written as an overview of the basic concepts most likely to be encountered in neuroeconomic research. The first part of the chapter introduces the reader to the basic concepts and philosophical underpinnings of game theory in relation to neuroeconomics. The second part is an introduction and discussion of common games, including the games featured in the other chapters of this book.

(Spade): If you kill me, how are you going to get the bird? If I know you can’t afford to kill me till you have it, how are you going to scare me into giving it to you?

(Gutman): “Well, sir, there are other means of persuasion besides killing and threatening to kill.”

(Spade): “Sure, but they’re not much good unless the threat of death is behind them to hold the victim down. See what I mean? If you try something I don’t like I won’t stand for it. I’ll make it a matter of your having to call it off or kill me, knowing you can’t afford to kill me.”

(Gutman): “I see what you mean. That is an attitude, sir, that calls for the most delicate judgment on both sides, because, as you know, sir, men are likely to forget in the heat of action where their best interests lie and let their emotions carry them away.”

—The Maltese Falcon

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Notes

  1. 1.

    Comprehensive, technical treatments can be found for example in Myerson (2013) and Osborne and Rubinstein (1994).

  2. 2.

    That is, games that can not be reduced to sets of mere one-player decision problems in which the actions of other players are irrelevant to each players utility.

  3. 3.

    Think for example of a secret ballot election, in which each player enters a vote into a computer, and the computer then decides the election outcome by considering all such submitted votes.

  4. 4.

    Note that all extensive form games can be transformed into normal form, but not all normal form games may have an equivalent extensive form; hence there also exists a qualitative difference.

  5. 5.

    Game theory divides games into cooperative and noncooperative types. All of the games in this chapter are noncooperative games, and we therefore do not spend a lot of time discussing the difference between the two classes of games, which can be found elsewhere (e.g., Myerson 2013).

  6. 6.

    The concept is named after John Nash, among other contributions, for his work on such equilibrium points in n-person games (Nash 1950).

  7. 7.

    Note that Economic Theory is primarily concerned with generalizable predictive validity, and that content validity regarding the process via which a decision is actually made, is at best secondary, but probably irrelevant, to as-if modeling in economics.

  8. 8.

    Rationality in the economic sense means that the decision-maker has preferences that are complete and transitive, or acyclical. This means that the decision-maker can rank all alternatives according to an ordinal metric, and that within this ranking whenever A is preferred to B, and B is preferred to C, then A will be preferred to C also.

  9. 9.

    Independent and identically distributed.

  10. 10.

    Economic models exist, which relate such behavior to rational choice under uncertainty (e.g., Neyman 1985; Kreps et al. 1982).

  11. 11.

    A sub-game is strictly defined as any subset of a game which has a uniquely identified initial node (i.e., the initial node does not share an information set with any other node), and contains all nodes that follow the initial node in the complete game as well as all successor nodes to these nodes. An additional condition is that all the nodes included in an information set of the sub-game must also be included in the sub-game.

  12. 12.

    For the values used in the schematic Fig. 2.5, the mixed strategy equilibrium has both players hunting the stag with probability 1/3 and the hare with probability 2/3.

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Authors and Affiliations

  1. Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, Netherlands

    Claudia Civai

  2. Institute of Food and Resource Economics, University of Bonn, Bonn, Deutschland

    Daniel R. Hawes

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  1. Claudia Civai
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  2. Daniel R. Hawes
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Correspondence to Claudia Civai .

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Editors and Affiliations

  1. Differentielle and Biologische Psychologie, Rheinische Friedrich-Wilhelms- Universität Bonn, Bonn, Germany

    Martin Reuter

  2. Department of Molecular Psychology, Institute for Psychology and Education, Ulm University, Ulm, Germany and Key Laboratory for NeuroInformation, School of Life Science and Technology, Center for Information in Medicine, University of Electronic Science and Technology of China, Chengdu, China

    Christian Montag

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Civai, C., Hawes, D.R. (2016). Game Theory in Neuroeconomics. In: Reuter, M., Montag, C. (eds) Neuroeconomics. Studies in Neuroscience, Psychology and Behavioral Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35923-1_2

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