Reflexive Decision and Game Theory

A new perspective on rationality The foundations of decision theory and game theory are commonly thought to be settled, yet there are many examples of human behaviour which is not rational in the way these theories describe. We spoke to Professor Wolfgang Spohn about his work in re-examining basic normative questions about rationality, which could shift the normative reference point for empirical research.

Our model of rational human behaviour has been fundamentally shaped by the development of modern decision theory and game theory. “The basics of these theories are thought to be somehow settled for decades – erroneously,” says Wolfgang Spohn, Professor of Philosophy and the Philosophy of Science at the University of Konstanz. The point is not that these theories are often conflated with the model of homo economicus, which assumes that we are primarily guided by rational self-interest and prioritise our own economic concerns.

Such assumptions about specific individual values do not belong to the basic conception of rationality. Still, there are many examples of human behaviour which seem rational, but are not regarded as such by standard decision and game theory. While most research

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tinkers round the edges of existing theory, Professor Spohn aims to re-examine the foundations of rationality in a new Reinhart Koselleck project. “The basic normative questions about rationality are not settled.

They are still contentious, and I want to take them in a specific direction,” he says.

Normative theory of rationality Professor Spohn’s inquiry into the foundations of a normative theory of rationality could fundamentally change the reference point for all empirical research. “Empirical research proceeds from the standard normative picture and then tries to find explanations for how and why we deviate. But if that standard reference point is not the correct one, then the focus of empirical research should shift,” he explains.

In traditional decision theory and game theory, formal structures called trees are used to represent different options of the agent and the various ways in which a situation may develop. “Two kinds of nodes are usually distinguished in a tree, the action nodes and the chance - or nature’s - nodes. I want to add a third kind of node, which I call decision nodes,” outlines Professor Spohn. “These decision nodes represent not the options of the agent, but rather the decision situations themselves that she is in, or may get into. They represent possible mental states in which she takes a decision and chooses an action.” The label ‘reflexive’ in the project’s title precisely refers to the reflection on those mental states.

The decision nodes as described are something that Professor Spohn believes should be additionally represented within

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theoretical frameworks, leading to a more general theory of rationality capable of dealing with a wider range of situations.

For instance, while standard theories only deal with the ways your decision situation may improve through the addition of more information, the more general theory can also deal with questions such as: How do you rationally behave today, when you expect to have forgotten something important tomorrow? How do you rationally take into account the fact that your preferences may be different tomorrow?

expressions for example. They therefore have an influence, particularly on social environments which are receptive to such influence. Again, the decision relevance of this aspect can only be captured in the reflexive perspective.

This point is best exemplified in applications to game-like social situations. Such situations involve several ‘players’, and the outcome depends on their behaviour. They may be opponents or partners, or be entangled in some other way. The prisoners’ dilemma is a famous example, because it is a very common social situation.

The basic normative questions about rationality are not settled. They are still contentious, and I want to take them in a specific direction.

Such questions call for a reflexive decision theory, modelling your reflection on your possible decision situations. Economists currently have only restricted models of preference change, an issue Professor Spohn is working to address.

Another important aspect is the fact that decision-relevant mental states not only lead to rational action but are also expressed in other ways, through speech, emotions and facial

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In the original scenario, two criminals are arrested, but the police don’t have sufficient evidence to convict them on the more serious of two charges, so need a confession from one or both. If neither of them confesses, they can only be tried for a minor crime. If both confess, they will be imprisoned for a long time. However, if only one confesses, he is set free as the chief witness, while the other, showing no repentance, is even more severely punished. “Thus, both

rationally confess. At least this is what all game theorists say,” says Professor Spohn.

The same social structure (reduced to two persons) is exemplified with the decision to get vaccinated in the table below. Both are better off when getting both vaccinated than both getting not vaccinated. But each is still better off when only the other one gets vaccinated. If so, both seem rational in not getting vaccinated.

In the original example, the two prisoners can’t communicate. They don’t see what the other does, so their actions are causally independent. “Standard game theory concludes from this that the two decisions are also probabilistically independent. However, that’s a mistake,” claims Professor Spohn.

The prisoners may have collaborated over the years and thus have developed an awareness of each other’s mentality, a kind of causally entangled, joint mental setup.

This causal entanglement creates a common cause structure of their actions (confessing or not confessing), thus rendering them probabilistically dependent, even though they are causally independent. Just as fever and cough are correlated, but do not cause each other; rather, both are caused by an infection.

“The standard solution concept of game

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Reflexive Decision and Game Theory Reflexive Decision and Game Theory Project Objectives

The project proceeds from the perspective that game and decision theory are normatively deficient, and attempts to improve the normative ideal of a homo economicus. This would shift the point of attack of empirical criticism.

The project does so by conceptualizing and theorizing `reflexive ascent’ in a formally rigorous way. According to it, a person considers not only her possible actions and their possible consequences, but also her possible (future) decision situations, which entail those actions.

Project Funding

The project is funded by the DFG (German Science Foundation) under the Grant No. SP 279/21-1 (Project No. 420094936).

Project Collaborators • Dr. Gerard Rothfus • Dr. Mantas Radzvilas

Project Partners

• Prof. Dr. Bernd Sturmfels, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany • Dr. Irem Portakal

Contact Details

Project Coordinator, Professor Wolfgang Spohn Department of Philosophy, University of Konstanz, 78457 Konstanz, Germany E: wolfgang.spohn@uni-konstanz.de W: https://www.philosophie.uni-konstanz. de/ag-spohn/ W: https://www.philosophie.uni-konstanz.de/ ag-spohn/personen/prof-dr-wolfgang-spohn/ Spohn, W. (2003), “Dependency Equilibria and the Causal Structure of Decision and Game Situations”, Homo Oeconomicus 20, 195-255 Kusser, A., W. Spohn (1992), “The Utility of Pleasure is a Pain for Decision Theory”, Journal of Philosophy 89, 10-29

Professor Wolfgang Spohn

theory, the Nash equilibrium, is characterised by the probabilistic independence of the individuals’ actions,” explains Professor Spohn.

He challenges this solution. “Despite causal independence, there may still be probabilistic dependence, and this is accounted for by another solution concept, which I call dependency equilibria,” he continues. “These dependency equilibria are more general than Nash equilibria. In particular, the prisoners may rationally cooperate - i.e. not confess - in such a dependency equilibrium.”

Two kinds of nodes are usually distinguished in a tree, the action nodes and the chance - or nature - nodes. I want to add a third kind of node, which I call decision nodes Normative reference point

Wolfgang Spohn is Professor emeritus of Philosophy and Philosophy of Science at the University of Konstanz and Senior Professor at the University of Tübingen. He was winner of the Lakatos Award in 2012. He is devoted to analytic philosophy and widely contributing to epistemology, philosophy of science, and the theory of theoretical and practical philosophy.

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response and adjust the split accordingly, which is borne out by the evidence. Researchers often observe a £5-£5 or £6-£4 split, while it’s unusual for a proposer to suggest a £9-£1 split, which game theory tells us to be the rational outcome.

“The ultimatum game is taken as a core example for other-regarding preferences. The proposer has a concern for fairness,” says Professor Spohn.

However, there are many dependency equilibria, i.e., rational outcomes in the ultimatum game, including an even split of the money. “This puts the existing literature in a different light,” he

The inclusion of dependency equilibria in game theory could lead to fundamental change by shifting the normative reference point for empirical research. This can be illustrated by the ultimatum game, where one individual (the proposer) receives, say, £10, which he has to split with somebody else (the responder). He may offer £1 (or more) and propose to keep £9 (or less). The responder can accept or reject this. If she accepts, she gets £1, if she rejects, nobody gets anything. Standard game theory claims that the responder will rationally accept the proposal, because £1 is better than nothing.

However, this is not what has been observed in experiments. If a proposer offers just £1 and keeps the rest for himself, the responder may well be outraged and reject the offer.

A proposer may then anticipate that kind of

says. “The rich experimental literature about the ultimatum game, and other similar games, would get a different reference point.”

This could eventually lead to changes in economic models. While his own background is in philosophy, Professor Spohn, who is a renowned formal epistemologist, has studied economic literature and regularly communicates with researchers in the field. “My collaborators are well versed in economics, and we aim to influence the economics community,” he adds. As the author of an influential paper on epistemic game theory in 1982, he also has a strong reputation among economists, which he hopes will help his new ideas gain traction.

“I aim to heighten awareness of the general reflexive perspective and in particular of the idea of these dependency equilibria not only in philosophy, but also amongst economists,” he says.

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