Online research in philosophy

We compare Colman's proposed “psychological game theory” with the existing literature on psychological games (Geanakoplos et al. 1989), in which beliefs and intentions assume a prominent role. We also discuss experimental evidence on intentions, with a particular emphasis on reciprocal behavior, as well as recent efforts to show that such behavior is consistent with social evolution.

I argue that standard decision theories, namely causal decision theory and evidential decision theory, both are unsatisfactory. I devise a new decision theory, from which, under certain conditions, standard game theory can be derived.

The objective of this paper is to construct an implementable theory of rational decision-making for cognitive agents subject to realistic resource constraints. It is argued that decision-making should select actions indirectly by selecting plans that prescribe them. It is also argued that although expected values provide the tool for evaluating plans, plans cannot be compared straightforwardly in terms of their expected values, and the objective of a realistic agent cannot be to find optimal plans. The theory of Locally Global planning is proposed as a realistic alternative to standard "maximizing" theories of rational decision-making.

This paper investigates decision-theoretic planning in sophisticated autonomous agents operating in environments of real-world complexity. An example might be a planetary rover exploring a largely unknown planet. It is argued th a t existing algorithms for decision-theoretic planning are based on a logically incorrect theory of rational decision making. Plans cannot be evaluated directly in terms of their expected values, because plans can be of different scopes, and they can interact with other previously adopted plans. Furthermore, in the real world, the search for optimal plans is completely intractable. An alternative theory of rational decision making is proposed, called “locally global planning”.

Decision-theoretic planning is normally based on the assumption that plans can be compared by comparing their expected-values, and the objective is to find an optimal plan. This is typically defended by reference to classical decision theory. However, classical decision theory is actually incompatible with this “simple plan-based decision theory”. A defense of plan-based decision theory must begin by showing that classical decision theory is incorrect insofar as the two theories conflict, so this paper begins by raising objections to classical decision theory . First, there is a discussion of the considerations arising out of the Newcomb problem that have given rise to causal decision theory. Next, counterexamples are constructed for classical decision theory turning on the fact that an agent may be unable to perform an action, and may even be unable to try to perform an action. A proposal is made for how to repair classical decision theory in light of these counterexamples. But then turning to the concept of an “alternative” that is presupposed by classical decision theory, it is argued that actions must often be chosen in groups rather than individually, i.e., the objects of rational choice are plans. It is argued that optimality cannot be defined for plans, and even if it could be, it would not be reasonable to require rational agents to find optimal plans. So simple plan-based decision theory must also be rejected. An alternative called “locally global planning” is proposed as a replacement for both classical decision theory and simple plan-based decision theory.

In this paper I study two ways of transforming decision problems on the basis of previously adopted intentions, ruling out incompatible options and imposing a standard of relevance, with a particular focus on situations of strategic interaction. I show that in such situations problems arise which do not appear in the single-agent case, namely that transformation of decision problems can leave the agents with no option compatible with what they intend. I characterize conditions on the agents’ intentions which avoid such problematic scenarios, in a way that requires each agent to take account of the intentions of others.

Game trees (or extensive-form games) were first defined by von Neumann and Morgenstern in 1944. In this paper we examine the use of game trees for representing Bayesian decision problems. We propose a method for solving game trees using local computation. This method is a special case of a method due to Wilson for computing equilibria in 2-person games. Game trees differ from decision trees in the representations of information constraints and uncertainty. We compare the game tree representation and solution technique with other techniques for decision analysis such as decision trees, influence diagrams, and valuation networks.

Games such as the St. Petersburg game present serious problems for decision theory.1 The St. Petersburg game invokes an unbounded utility function to produce an infinite expectation for playing the game. The problem is usually presented as a clash between decision theory and intuition: most people are not prepared to pay a large finite sum to buy into this game, yet this is precisely what decision theory suggests we ought to do. But there is another problem associated with the St. Petersburg game. The problem is that standard decision theory counsels us to be indifferent between any two actions that have infinite expected utility. So, for example, consider the decision problem of whether to play the St. Petersburg game or a game where every payoff is $1 higher. Let’s call this second game the Petrograd game (it’s the same as St. Petersburg but with a bit of twentieth century inflation). Standard decision theory is indifferent between these two options. Indeed, it might be argued that any intuition that the Petrograd game is better than the St. Petersburg game is a result of misguided and na¨ıve intuitions about infinity.2 But this argument against the intuition in question is misguided. The Petrograd game is clearly better than the St. Petersburg game. And what is more, there is no confusion about infinity involved in thinking this. When the series of coin tosses comes to an end (and it comes to an end with probability 1), no matter how many tails precede the first head, the payoff for the Petrograd game is one dollar higher than the St. Petersburg game. Whatever the outcome, you are better off playing the Petrograd game. Infinity has nothing to do with it. Indeed, a straightforward application of dominance reasoning backs up this line of reasoning.3 Standard decision theory.

Counterexamples are constructed for classical decision theory, turning on the fact that actions must often be chosen in groups rather than individually, i.e., the objects of rational choice are plans. It is argued that there is no way to define optimality for plans that makes the finding of optimal plans the desideratum of rational decision-making. An alternative called “locally global planning” is proposed as a replacement for classical decision theory. Decision-making becomes a non-terminating process without a precise target rather than a terminating search for an optimal solution.

It is suggested that there is a strong connection between intentions and plans, and these plans are then taken to be programs of the sort suggested by Miller, Galanter, and Pribram in Plans and the Structure of Behavior. There is then a hierarchy of programs connected with intentions stretching from the macroscopic level of ordinary discourse to the neurological level. It is argued that as we proceed downwards we arrive at a threshold below which we can still describe the phenomena but below which we can no longer speak of intentions. The paper concludes with a discussion of the criteria for the identity of intentions at various levels.