Spieltheorie

Worum es geht

The mathematical study of strategic interaction: situations where each actor's best choice depends on the choices of others. Founded by von Neumann (minimax, 1928) and the von Neumann-Morgenstern treatise (1944), generalised by Nash's equilibrium (1950), deepened by Selten (credibility), Harsanyi (incomplete information), Schelling (coordination and commitment) and Aumann (repeated games), extended to biology by Maynard Smith and to institution-building by mechanism design. Since the 1980s the discipline has been the language of microeconomic theory — while experiments and internal skeptics dispute how much of observed behaviour it predicts.

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• Is game theory a predictive science of behaviour, a normative logic of strategy, or a collection of illuminating fables?

  4 benannte Positionen · unresolved; every serious course now has to say which reading it teaches

• Do laboratory deviations refute equilibrium analysis or merely refine its domain?

  4 benannte Positionen · live; the experimental facts are accepted, their meaning is not

• With multiple equilibria everywhere, which one — and did the refinement program answer the question?

  4 benannte Positionen · unresolved; the multiplicity problem is the field's oldest open wound

• Did Axelrod's tournaments establish that reciprocity solves the problem of cooperation?

  4 benannte Positionen · reciprocity remains a central mechanism, its sufficiency and the tournament's generality are contested

• Is backward induction — the logical core of sequential analysis — actually justified, and do people follow it?

  5 benannte Positionen · logically clarified, behaviourally decided against the naive prediction; teach the theorem with its failure record

Mythen, die das Paket korrigiert

Verbreitete Behauptungen mit der Evidenz, die sie klärt oder begrenzt.

• “Game theory is about board games and gambling — a recreational branch of mathematics.”

  debunked

  The subject is strategic interdependence in general: oligopoly pricing, wage bargaining, deterrence, auctions, animal conflict, protocol design. Von Neumann and Morgenstern's 1944 title says it directly — Theory of Games AND Economic Behavior — and the treatise's stated aim is the foundations of economics. Parlour games were the fruit-fly, not the topic.

• “Game theory assumes — or proves — that people are selfish.”

  debunked-as-general-rule

  Payoffs are von Neumann-Morgenstern utilities and can encode altruism, fairness, spite or duty; the machinery is preference-neutral. What experiments like the ultimatum game reject is the auxiliary assumption that utility equals own money — proposers offer near-even splits and responders reject low offers across hundreds of replications. Whether to model that as social preferences inside standard theory (Fehr & Schmidt, Quarterly Journal of Economics 1999) or as a deeper failure is the live debate; "game theory proved selfishness" is wrong on both readings.

• “A Nash equilibrium is the best possible outcome — equilibrium play means everyone is doing well.”

  debunked

  Equilibrium means mutual best response — no profitable unilateral deviation — and nothing more. The prisoner's dilemma equilibrium is strictly worse for both players than mutual cooperation; coordination games have Pareto-ranked equilibria where the bad one is perfectly stable. The gap between equilibrium and efficiency is the starting point of welfare analysis and mechanism design, not a footnote.

• “The bar scene in the film A Beautiful Mind explains Nash equilibrium.”

  debunked

  In the scene, everyone ignoring the most sought-after woman is not a Nash equilibrium of the situation as narrated: any single man gains by deviating and approaching her, which is precisely what the definition rules out. The scene dramatises a cooperative agreement, closer to the collusive outcomes Nash's own concept explains as unstable. Check the claim directly against the two-line definition in Nash's 1950 note; standard microeconomics courses use the scene as a spot-the-error exercise. Nasar's biography, unlike the film, states the mathematics correctly.

• “Axelrod proved that tit-for-tat is the best strategy for the repeated prisoner's dilemma.”

  debunked-as-general-rule

  There is no best strategy independent of the opposing population, and Axelrod's own text says so — tit-for-tat won two particular tournaments against particular entrant pools and never beats any opponent in a single match. Under noise it unravels into vendettas: more generous variants (Molander, Journal of Conflict Resolution 1985) and win-stay-lose-shift (nowak-sigmund-1993, Nature) outperform it in evolutionary settings. The folk theorem (fudenberg-maskin-1986) shows the repeated game supports a vast set of equilibria, cooperative and not — which one prevails is a selection question the tournaments alone cannot settle.