Utility, Games, and Narratives

Appendices

Further Reading

Game Theory is a huge subject. Relevant handbooks are Aumann and Hart (1992, 1994, 2002) and, at a more introductory level, Rasmusen (2007). However, agent-based modelers should keep in mind that a substantial part of Game Theory has been developed around equilibrium states, which are generally not a main concern for agent-based modelers. Evolutionary games, thoroughly discussed in the above handbooks, are possibly closest to agent-based modeling. For other evolutionary mechanism, see Chap. 18 in this volume (Chattoe-Brown and Edmonds 2013).

Neural networks are a huge subject as well. This field is currently split in two streams: On the one hand, research on neural networks as a model of cognitive processes in the brain. On the other hand, research on neural networks as an engineering tool for signal processing. A handbook oriented towards cognitive problems is Arbib (2002). Handbooks oriented towards engineering problems are Hu and Hwang (2002) and Graupe (2007). Specifically, unsupervised neural networks are often employed in pattern recognition. A comprehensive treatment of pattern recognition techniques is Ripley (1996).

All other tools and issues discussed in this chapter are in their infancy, so no generic reading can be mentioned. Interested scholars are better advised to start with the original papers mentioned in the bibliography, tracking developments on recent publications and working papers.

Reasoned Bibliography

This chapter covered too many topics to be able to provide detailed references. Henceforth, a few basic publications will be listed, that may be used by interested readers as a first orientation to each of the topics mentioned in this chapter.

2.1 Utility and Games

Utility maximization was pioneered by Frank Ramsay and Bruno De Finetti in the 1930s, and subsequently refined by Leonard Savage in the 1950s. Savage still provides the most comprehensive explanation of this approach to uncertain reasoning.

Game Theory was initiated by John Von Neumann and Oskar Morgenstern in the 1940s. It subsequently developed into a huge research field within economics, with several specialized journals. Today, game theory is a field characterized by extreme mathematical sophistication and intricate conceptual constructions.

This chapter did not focus on the assumptions and methods of Game Theory, but rather aimed at presenting the main prototypical games that have been devised hitherto. A classical treatise by Duncan Luce and Howard Raiffa may introduce the subject more easily than Von Neumann and Morgenstern did. Luce and Raiffa were first to present the Battle of the Sexes as well as the Prisoner’s Dilemma, which they ascribed to Albert Tucker anyway.

Readers interested in evolutionary games may rather read the treatises written by Jörgen Weibull and Herbert Gintis, respectively. The former is more specific on evolutionary games, but also more technical than the second one.

Robert Axelrod is the main reference so far it regards simulations of the iterated Prisoner’s Dilemma with retaliation strategies. The idea that the iterated Prisoner’s Dilemma could yield cooperation simply relying on tags is due to Rick Riolo.

The Stag Hunt and the Game of Chicken are classical, somehow commonsensical games. The Game of Chicken has been turned into the Hawk-Dove Game by Maynard Smith and George Price. The Hawk-Dove game is not terribly different from The War of Attrition, conceived by Maynard Smith and improved by Timothy Bishop and Chris Cannings.

The Traveller’s Dilemma and The Dollar Auction are recent games invented by Kaushik Basu and Martin Shubik, respectively. Pure Coordination games have been discovered by Thomas Schelling.

Axelrod RM (1984) The evolution of cooperation. Basic Books, New York

Basu K (1994) The traveller’s dilemma: paradoxes of rationality in game theory. Am Econ Rev 84:391–395

Bishop DT, Cannings C, Smith JM (1978) The war of attrition with random rewards. J Theor Biol 74:377–389

Gintis H (2000) Game theory evolving. Princeton University Press, Princeton

Luce RD, Raiffa H (1957) Games and decision: introduction and critical survey. Wiley, New York

Riolo RL, Cohen MD, Axelrod RM (2001) Evolution of cooperation without reciprocity. Nature 414:441–443

Savage L (1954) The foundations of statistics. Wiley, New York

Schelling TC (1960) The strategy of conflict. Harvard University Press, Cambridge, MA

Shubik M (1971) The dollar auction game: a paradox in noncooperative behavior and escalation. J Conflict Resolut 15:109–111

Smith JM, Price GR (1973) The logic of animal conflict. Nature 246:15–18

Weibull J (1997) Evolutionary game theory. The MIT Press

2.2 Influence Games

Ernst Ising introduced his model in the 1920s. Since then, a huge literature appeared.

The Ising model is taught in most Physics courses around the world, so a number of good introductions are available on the Internet. A printed introduction by Barry Cipra is mentioned here for completeness.

Schelling’s model of racial segregation was developed independently of the Ising model. However, it may be considered a variation of it.

The El Farol Bar Problem was conceived by Brian Arthur. Renamed The Minority Game and properly formalized, it was introduced to physicists by Damien Challet and Yi-Cheng Zhang.

A huge literature on the Minority Game has appeared on Physics journals. Good introductions have been proposed, among others, by Esteban Moro and Chi-Ho Yeung and Yi-Cheng Zhang.

Arthur WB (1994) Inductive reasoning and bounded rationality. Am Econ Rev 84:406–411

Challet D, Zhang YC (1997) Emergence of cooperation and organization in an evolutionary game. Phys A 246:407–418

Cipra BA (1987) An introduction to the Ising model. The American Mathematical Monthly 94:937–959

Moro E (2004) The minority game: an introductory guide. In: Korutcheva E, Cuerno R (eds) Advances in condensed matter and statistical physics. Nova Science Publishers, New York, pp 263–286. (Also available online at http://arxiv.org/abs/cond-mat/0402651v1)

Schelling TC (1971) Dynamic models of segregation. J Math Sociol 1:143–186

Yeung CH, Zhang YC (2009) Minority games. In: Meyers RA (ed) Encyclopedia of complexity and systems science. Springer, Berlin. (Also available online as http://arxiv.org/abs/0811.1479v2)

2.3 Some Pitfalls of Utility Maximization

The idea that probabilities measured on samples of size zero are somewhat awkward is quite old, and evidently linked to the frequentist view of probabilities. Daniel Ellsberg circulated this idea among economists, where in the meantime the subjectivist view of probability judgements had become dominant. Sub-additive probabilities were conceived by Bernard Koopman in the 1940s and popularized among economists by David Schmeidler in the 1980s.

Maurice Allais submitted his decision problem to Leonard Savage, who did not behave according to his own axioms of rational choice. Since then, Savage presented utility maximization as a normative, not as a descriptive theory. Prospect Theory was advanced by Daniel Kahneman and Amos Tversky; it comes in a first version (1953), and a second version (1992).

The preference reversals highlighted by Paul Slovic have triggered a huge literature. A recent book edited by Sarah Lichtenstein and Paul Slovic gathers the most important contributions.

Kenneth Arrow originally devised his paradox as a logical difficulty to the idea of a Welfare State that would move the economy towards a socially desirable equilibrium. However, it may concern any form of group decision-making.

Michael Mandler is the main reference for a possible conciliation of Slovic’s and Arrow’s paradoxes with utility maximization, provided that preferences are incomplete.

Allais M (1953) Le comportement de l’homme rationnel devant le risque: critique des postulats et axiomes de l’école americaine. Econometrica 21:503–546

Arrow KJ (1950) A difficulty in the concept of social welfare. J Polit Econ 58:328–346. (Reprinted in The collected papers of Kenneth J. Arrow. Blackwell, Oxford, 1984)

Ellsberg D (1961) Risk, ambiguity, and the savage axioms. Quart J Econ 75:643–669

Kahneman D, Tversky A (1953) Prospect theory: an analysis of decision under risk. Econometrica 21:503–546

Koopman BO (1940) The axioms and algebra of intuitive probability. Annal Math 41:269–292

Lichtenstein S, Slovic P (2006) (eds) The construction of preference. Cambridge University Press, Cambridge

Mandler M (2005) Incomplete preferences and rational intransitivity of choice. Games Econ Behav 50:255–277

Savage L (1967) Difficulties in the theory of personal probability. Philos Sci 34:305–310

Schmeidler D (1989) Subjective probability and expected utility without additivity. Econometrica 57:571–587

Tversky A, Kahneman D (1992) Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertainty 5:297–323

2.4 Logic of Consequence and Logic of Appropriateness

An introduction and thorough discussion of the differences between the logic of consequence and the logic of appropriateness can be found in a book by James March, A Primer on Decision Making. The same Author, in 1974 and 1976, has been the first to point to the fact that human beings distort their memories of the past in order to construct coherent stories that guide them into the future. This point has been also made by Karl Weick, who wrote a lengthy treatise on this subject a few decades later.

A number of psychological experiments confirm this idea. Interested readers may start with the works of Daryl Bem, Michael Conway, Michael Ross and a book edited by Ulric Neisser and Robyn Fivush.

However, the trouble with the idea of human beings reconstructing the past is that they are not willing to concede that they do so. Thus it is extremely difficult to find case-studies. The one by David Lane and Robert Maxfield is possibly the only exception, though they were not allowed to published all the material they gathered during their investigation (Lane, personal communication).

A final remark on lack of communication in this stream of research. James March, Karl Weick and David Lane worked independently, possibly unaware of one another, focusing on the same issue but employing different expressions.

Bem DJ (1966) Inducing belief in false confessions. J Pers Soc Psychol 3: 707–710

Bem DJ (1967) Self-perception: an alternative interpretation of cognitive dissonance phenomena. Psychol Rev 74:183–200

Cohen MD, March JG (1974) Leadership and ambiguity: the American College President. McGraw-Hill, New York

Conway M, Ross M (1984) Getting what you want by revising what you had. J Pers Soc Psychol 47:738–748

Greenwald A (1980) The totalitarian ego: fabrication and revision of personal history. Am Psychol 35:603–618

Lane DA, Maxfield RR (2005) Ontological uncertainty and innovation. J Evolut Econ 15:3–50

March JG (1994) A primer on decision making. The Free Press, New York

March JG, Olsen JP (1976) Organizational learning and the ambiguity of the past. In: March JG, Olsen JP (eds) Ambiguity and choice in organizations. Universitetsforlaget, Bergen

Neisser U, Fivush R (1994) (eds) The remembering self: construction and accuracy in the self-narrative. Cambridge University Press, Cambridge

Ross M, Newby-Clark IR (1998) Costructing the past and future. Soc Cognit 16:133–150

Weick KE (1979) The social psychology of organizing. Random House, New York

Weick KE (1995) Sensemaking in organizations. Sage, Thousand Oaks

2.5 Tools for the Logic of Appropriateness

This chapter did not deal with tools where categories pre-exist to the information that is being received, namely, supervised neural networks and Case-Based Decision Theory. Readers interested in supervised neural networks may start with the classical handbook by Rumelhart, McClelland and the PDP Research Group. Readers interested in Case-Based Decision Theory may refer to a series of articles by Izhak Gilboa and David Schmeidler.

The earliest intuitions on the nature of mental categories date back to Ludwig Wittgenstein. A good explanation of the main features of mental categories, and why they are so different from our common idea of what a “category” is, is provided by George Lakoff in his Women, Fire, and Dangerous Things.

So far it regards unsupervised neural networks, the classic book by Teuvo Kohonen is still unrivaled for its combination of mathematical rigour and philosophical insight. Having been written at an early stage, it still keeps a strong link between artificial neural networks and the human brain.

Paul Thagard is the basic reference for constraint satisfaction networks. Constraint satisfaction networks appear in several contributions to the book The Construction of Preference, edited by Sarah Lichtenstein and Paul Slovic, mentioned in the section “Some Pitfalls of Utility Maximization”. Regarding the importance of focussing on two alternatives in order to arrive at a decision, see a working paper by Guido Fioretti.

Evidence Theory started with a book by Glann Shafer in 1976, and triggered a small but continuous flow of mathematical works since then. An article by Guido Fioretti explains it to social scientists, along with examples of applications to decision problems.

Fioretti G (2009) Evidence theory as a procedure for handling novel events. Metroeconomica 60:283–301

Fioretti G (2011) Either, or: exploration of an emerging decision theory (Working paper). http://ssrn.com/abstract=1314352

Gilboa I, Schmeidler D (1995) Case based decision theory. Quart J Econ 110:605–639

Kohonen T (1989) Self-organization and associative memory. Springer, Berlin

Lakoff G (1987) Women, fire, and dangerous things. University of Chicago Press, Chicago

Rumelhart DE, McClelland JL, The PDP Research Group (1986) Parallel distributed processing: explorations in the microstructure of cognition. MIT Press, Cambridge, MA

Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton

Thagard P (2000) Coherence in thought and action. MIT Press, Cambridge, MA