Fragmentation and Information Access

Is there an English word that ends in ‘MT’? (If you are stumped, think about it for a moment and then read the last word of this abstract.) Before you figured out (or read) the answer to that question, did you possess the information that the word that is the answer is an English word that ends in ‘MT’? In a sense, yes: the word was in your vocabulary. But in another sense, no: perhaps you weren’t able to immediately answer the puzzle question. For finite agents, this phenomenon is unavoidable. We often possess a piece of information for some purposes (or with respect to some elicitation conditions) but not for other purposes (or conditions). This suggests that a mental state be represented not by a single batch of information, but rather by an ‘access table’—a function from purposes to batches of information. This representation makes clear what happens during certain ‘aha!’ moments in reasoning. It also allows us to model agents who exhibit imperfect recall, confusion, and mental fragmentation. And it sheds light on the difference between propositional knowledge and knowledge-how. The upshot is that representing mental states using access tables is more fruitful than one might have dreamt.

Automated Construction of Bounded-Loss Imperfect-Recall Abstractions in Extensive-Form Games (Extended Abstract)

Information abstraction is one of the methods for tackling large extensive-form games (EFGs). Removing some information available to players reduces the memory required for computing and storing strategies. We present novel domain-independent abstraction methods for creating very coarse abstractions of EFGs that still compute strategies that are (near) optimal in the original game. First, the methods start with an arbitrary abstraction of the original game (domain-specific or the coarsest possible). Next, they iteratively detect which information is required in the abstract game so that a (near) optimal strategy in the original game can be found and include this information into the abstract game. Moreover, the methods are able to exploit imperfect-recall abstractions where players can even forget the history of their own actions. We present two algorithms that follow these steps -- FPIRA, based on fictitious play, and CFR+IRA, based on counterfactual regret minimization. The experimental evaluation confirms that our methods can closely approximate Nash equilibrium of large games using abstraction with only 0.9% of information sets of the original game.

Probabilistic Strategy Logic

We introduce Probabilistic Strategy Logic, an extension of Strategy Logic for stochastic systems. The logic has probabilistic terms that allow it to express many standard solution concepts, such as Nash equilibria in randomised strategies, as well as constraints on probabilities, such as independence. We study the model-checking problem for agents with perfect- and imperfect-recall. The former is undecidable, while the latter is decidable in space exponential in the system and triple-exponential in the formula. We identify a natural fragment of the logic, in which every temporal operator is immediately preceded by a probabilistic operator, and show that it is decidable in space exponential in the system and the formula, and double-exponential in the nesting depth of the probabilistic terms. Taking a fixed nesting depth, this gives a fragment that still captures many standard solution concepts, and is decidable in exponential space.

Imperfect Recall: The Politics of Subnational Office Removals

Why do some citizens remove the same politicians that they elected from office? This article examines the use of recall referenda, an increasingly prevalent process in which citizens organize a vote to remove politicians from office before they complete their terms. Although celebrated as a tool to improve electoral accountability, we argue that recall referenda are organized to pursue political vendettas. We test this claim using an original data set on the different stages leading to subnational recalls in Peru. Recalls are initiated more often when politicians lose by narrow vote margins and when women hold office. Once put to a vote, citizens do use office performance to decide whether to retain their politicians. Losing politicians organized fewer recall referenda following an institutional reform that allowed politicians to name their successors. The implication is that recall referenda create weak incentives to improve office performance, but careful institutional design can improve their functioning.

Alternating-time Temporal Logic on Finite Traces

We develop a logic-based technique to analyse finite interactions in multi-agent systems. We introduce a semantics for Alternating-time Temporal Logic (for both perfect and imperfect recall) and its branching-time fragments in which paths are finite instead of infinite. We study validities of these logics and present optimal algorithms for their model-checking problems in the perfect recall case.