Overmathematisation in game theory: pitting the Nash Equilibrium Refinement Programme against the Epistemic Programme
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studies in History and Philosophy of Science Part A 40 (3):290-300 (2009)
The paper argues that the Nash Equilibrium Refinement Programme in game theory was less successful than its competitor, the Epistemic Programme (Interactive Epistemology). The prime criterion of success is the extent to which the programmes were able to reach the key objective guiding non-cooperative game theory for much of the 20th century, namely, to develop a complete characterisation of the strategic rationality of economic agents in the form of the ultimate game theoretic solution concept for any normal form and extensive game. The paper explains this in terms of unjustified degrees of mathematisation in the Nash Equilibrium Refinement Programme. While this programme's mathematical models were often inspired by purely mathematical concerns rather than the economic phenomena they were intended to be mathematical models of, the Epistemic Programme's mathematical models were developed with a keen eye to the role beliefs and desires play in strategic interaction between rational economic agents playing games; that is, their Interactive Epistemology. The Epistemic Programme succeeded in developing mathematical models formalising aspects of strategic interaction that remained implicit in the Nash Equilibrium Refinement Programme due to an unjustified degree of mathematisation. As a result, the Epistemic Programme is more successful in game theory .
|Keywords||nash equilibrium refinement epistemic programme interactive epistemology game theory rationality economics mathematical modelling mathematisation|
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