Can we apply game-theoretic analysis to real life?
1. Introduction
Whenever the expected utilities of one agent’s choices depend on another agent’s decision, such an interaction can be modelled as a game and analysed through the lens of game theory (GT) (cf. Binmore 2007b, p. 3 – 5). Despite its theoretical success many academics and “practical men of business used to dismiss game theory as just one more ineffectual branch of social science” (cf. Binmore 2007a, p.2) and spiting the practical successes in areas like auctions – many continue to do so (cf. Syll 2018, p.45).
Empirically, this scepticism is supported by famous experiments in which experienced game theorists turned out to be no better at forecasting than students (cf. Goodwin 2002; Green 2005). Moreover, in experiments, GT seems to successfully predict behaviour only when certain criteria such as simplicity, adequate incentives and familiarity with the game are satisfied (cf. Binmore 2007b p. 65). But experiments aren’t real life. As the replication crisis suggests, one should not hastily generalize results of experiments involving such complex and diverse beings as humans (cf. Yarkoni 2020).
Outside experiments GT seems to have more empirical success. Especially in biology, it is quite good in predicting strategic behaviour like nepotism, reciprocity, mate selection etc. among animals (cf. Ross 2023, p. 129). Regarding human affairs: RAND game theorists have been shaping US Policy successfully to prevent nuclear war (cf. Emery 2021) – well, so far. It may be bit early to judge this a definite success (cf. Lindelauf 2021, p. 422). But even if global nuclear annihilation should falsify this hypothesis, GT still excels by predicting the behaviour of fish (cf. Hugie & Dill 1994).
The theoretical criticism is less fuzzy, as it often boils down to the straightforward question, whether the assumptions underlying GT hold in real life; whether it is able to say anything of significance about our lives despite being a tautological system (cf. Syll 2018, p.45).
Thus, this essay examines the following question: Do assumptions that are needed for a game-theoretic analysis of our actions hold in real life?, boiling down the answer to a simple: Yes and No. Or as the influential saying goes: In Theory There Is No Difference Between Theory and Practice, While In Practice There is (cf. O’Toole 2018).
2. Clarifying the question
2.1 Which game theory?
We need to clarify the assumptions underlying our question. GT isn’t a monolith, but a branch of decision theory. Since its first mathematical formulation by von Neumann and Morgenstern in 1944, this branch has seen continuous development and divergence into countless twigs – from pure orthodoxy to evolutionary and behavioural GT (cf. Ross 2023, pp. 2, 34). It also doesn’t appear to be complete yet (ibid. p. 36). The answer may therefore vary depending on the version of GT. For the sake of simplicity, this essay is mainly concerned with orthodox or pure GT as upheld by Binmore, among others (cf. Guala 2006, p. 241).
2.2 What analysis and which assumptions?
Following Revealed Preference Theory and orthodoxy, pure GT can be seen as a branch of mathematics, treating rationality as a technical concept of economic or instrumental rationality and only providing a set of analytical truths and tautologies – which can’t be refuted by empirical observations (cf. Syll 2018, p.45; Ross 2023, pp. 14, 17, 39). Following this view GT does always hold in real life in the sense that it can show us, how agents deviate from rationality, and provide some explanations of behaviour. Rational solutions of games or Nash equilibria are than not predictions of empirical reality, but only tools for analysis – describing endogenously stable states, which in reality are never isolated from exogenous factors (cf. Ross 2023, p. 34).
If we mean by holding in real life, that GT can be used to explain, prescribe and predict real human strategic reasoning, the assumptions underlying GT cause significant issues (cf. ibid. p.14) because orthodox GT as a mathematical endeavour lacks empirical content. When using GT to analyse reality, one can only do so by incorporating auxiliary assumptions about the empirical world into the modelling (cf. ibid. p.128). This is there the trouble arises.
3. Reality defying assumptions
3.1. Unified players
GT implicitly assumes unified agents as players. Such players are rather rare, and if they exist at all, they are found e.g. among insects and fish, whose behaviours GT can predict effectively with some auxiliaries from biology (cf. ibid. pp. 129, 130). Highly complex and cognitive plastic humans in contrast, appear to consist of several internal systems, deviating significantly from unified agents (cf. ibid. p. 131).
This isn’t necessarily a problem for GT itself, but for its application. This insight is the springboard for GTs relevance in neuroeconomics, where it is used not to analyse human actions, but the actions of systems inside humans, down to singular neurons (cf. ibid. pp. 139 -144). The results so far seem to provide some empirical vindication of GT (cf. ibid. p. 142). But if we mean with real life our phenomenological realities and with our actions more palpable interactions between humans, it appears a bit farfetched to call this holding.
3.2 Unbounded Rationality
GT makes strict assumptions of rationality and is only able to predict the behaviour of rational players (cf. Binmore 2007a, p.1). In real life, no such perfectly rational agents exist. We humans try to be rational, but our rationality is bounded, with limited time, knowledge and compute, (cf. Todd & Gigerenzer 2000, p. 728) and relays on heuristics, which cause biases (cf. ibid. pp. 734 – 739).
Nevertheless, GT itself may here be helpful to explain, why humans behave irrationally. With auxiliary assumptions from evolutionary psychology, GT seems to explain how moral intuitions and norms may have evolved as heuristics to solve coordination and equilibrium selection problems (cf. Binmore 2011a, p. 13 -15; cf. Joyce 2007, pp. 24 – 44) – without recursions to dubious metaphysics.
3.3 Confusing Map and Territory
The main issue is the ludic fallacy: when thinking about GT or applying it, people tend to mistake the map for the territory, the game for reality (cf. Taleb p.127). This implicit belief in no differences between model and world, theory and practice, is a priori wrong.
When creating games, theorists justify the design as stripped of all the irrelevant clutter (cf. Binmore 2007b, p.4). But: What is irrelevant and what not?
Reductionist models are a box, inside which our thinking may become trapped. Successful strategic action in reality – bypassing the Ligne Maginot – often depends on thinking outside boxes. Also changing rules – e.g. by burning your army’s ships, making retreat impossible, as generals did throughout history, from Alexander to Cortés – is what brilliant strategists appear to do in real life instead of blindly surrendering to a given Nash Equilibrium (cf. Ross 2023, pp. 3,4). Furthermore a huge part of strategic interactions is intelligence work – gathering information on the environment and on the other parties to gain an advantage in evaluating possible moves, but also feeding your opponents with false information to disadvantage them.
While mechanism design, the manipulation of rules top-down to alter the payoffs and rules of games, is one of the main areas of application for GT (cf. Binmore 2007b, p. 32), manipulation bottom-up by the players, is seldom considered and hard to model. There are approaches like dynamic GT (cf. Başar 2018), but modelling unknown exogenous variables is impossible.
Although theorists only assume perfect information among players for simple games (cf. Ross 2023 p.21), they seem to implicitly assume complete information on the side of themselves while modelling the utilities, probabilities and rules, circumventing the real-life issues of uncertainty and opacity by reformulating interactions as Bayesian games (cf. Başar 2018, p. 55) or using the subjective expected utility theory by Savage, again resorting to Bayesian probability (cf. Ross 2023, p. 71, 116). This is an issue:
1. Consequences are never known with certainty in real life. Here, rational estimates of informational structure, expected utilities and strategy sets are difficult to make and can change due to exogenous factors – reality is not a so-called small world; Bayesian principles are not plausible here (cf. ibid.).
2. Such models often fail to capture that in reality strategic behaviour makes heavy use of deception. In the context of mating, this has probably been common knowledge since the emergence of make-up in the Stone Age (cf. Kramberger et al. 2021) and for warfare, Sun Tzu pointed this out two millennia ago (cf. Tzu 2000, p.3). Sure, theorists can and do model sometimes deception in games, e.g. when modelling Poker, they incorporate bluffing (cf. Binmore 2007b, 432), but they usually don’t incorporate options like cheating or distracting opponents with a flirt, as they stay inside the box of formal rules. This implicit assumption, that games capture all relevant data, may lead to biased and boxed thinking.
An example of this inside-the-box-thinking is the St. Petersburg-Paradox, where theorists wonder, why most people wouldn’t pay much for a game of coin-flipping with an expected utility of infinity (cf. Peterson 2023). What they usually fail to consider is that, in real life, the offer to play a gamble with an expected infinite payoff can’t be anything else than a scam (cf. ibid.). Only fools would intuitively trust such a shady offer.
Another example is the classic prisoner’s dilemma (PD) (cf. Binmore 2007a, p. 15 – 19). Many critics of GT fall themselves for the ludic fallacy, when they argue, that confessing in the PD can’t be the solution. But it is (cf. ibid.). Given all the restrictions of the PD, the rational, dominant strategy in such a situation would be to confess. But: The situation described in the PD could never occur in reality.
In real life there would be many more options than confessing or staying silent: lying, confessing partially, feigning insanity or an appendicitis and escaping from the ER, threatening the interrogator etc. The consequences of decisions would be more numerous and uncertain than just fixed prison years. The two criminals are also not the only players. Others, especially the interrogators and peers, are players too. While GT can explain why the prisoners can’t trust each other (cf. Ross 2023, pp. 28 – 29), there is no obvious reason, why they should trust the interrogators. Confessing in reality may not only not spare you prison time as the offer could be a trick – it may also destroy your reputation, end with a knife in yours or a loved one’s throat. It may even end with no chance for your lawyer to bribe the judge to rule in dubio pro reo.
Most game theorists argue that this is not an issue for GT, as in real life we just play different games than the PD (cf. Binmore 2015). This is true. If we want to apply GT to real situations, we have to model them right. Every relevant choice and consequence must be incorporated into the game. But: Such certain knowledge about reality usually isn’t available. Even if it were, it would make the games so large, that they would be either impractical or decline in predictive power due to capturing too much noise. To put it in statistical terms: While models based on pure GT seem to be underfitting, the necessary addition of auxiliary assumptions may lead to partial overfitting (cf. Christian & Griffiths 216, pp. 154, 233) – and ways to solve this issue are beyond the scope of GT and this essay.
3. Conclusion
In a practical sense the assumptions needed for game-theoretic analysis of our actions don’t hold well in real life outside of specific contexts e.g. auctions and fish. While GT can be a powerful tool to analyse real behaviour, to do so one must abandon some core assumptions of pure GT e.g. unbounded rationality, but also employ auxiliary assumptions about the world. GT constitutes therefore a double-edged sword – while it can sharpen our strategic thinking and provide explanations; it needs auxiliaries and may cloud our judgment with the ludic fallacy, trapping our mind in misfitting boxes.
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2 of 4 Essay for the course: Rational agents in social interaction
Lecturer: Dr. Jurgis Karpus
LMU University of Munich
