Related papers: Repetition in Permutation Wordle
Large language models (LLMs) are increasingly deployed to support human decision-making. This use of LLMs has concerning implications, especially when their prescriptions affect the welfare of others. To gauge how LLMs make social…
We investigate symmetric equilibria of mutual reinforcement learning when both players alternately learn the optimal memory-two strategies against the opponent in the repeated prisoners' dilemma game. We provide a necessary condition for…
We study an information-structure design problem (a.k.a. persuasion) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal distributions. As in the standard…
In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor. Since a single neighbor is taken as reference, the information stemming from other neighbors is neglected, which…
How can we generate a permutation of the numbers $1$ through $n$ so that it is hard to guess the next element given the history so far? The twist is that the generator of the permutation (the ``Dealer") has limited memory, while the…
The technique of guessing can be very fruitful when dealing with sequences which arise in practice. This holds true especially when guessing is performed algorithmically and efficiently. One highly useful tool for this purpose is the…
We consider the structure of roller coaster permutations as introduced by Ahmed & Snevily[1]. A roller coaster permutation is described as a permuta- tion that maximizes the total switches from ascending to descending or visa versa for the…
Imitation is simple behavior which uses successful actions of others in order to deal with one's own problems. Because success of imitation generally depends on whether profit of an imitating agent coincides with those of other agents or…
We study a robust Dynkin game over a set of mutually singular probabilities. We first prove that for the conservative player of the game, her lower and upper value processes coincide (i.e. She has a value process $V $ in the game). Such a…
Game-theoretic dynamics between AI agents could differ from traditional human-human interactions in various ways. One such difference is that it may be possible to accurately simulate an AI agent, for example because its source code is…
Naming game simulates the process of naming an objective by a population of agents organized in a certain communication network topology. By pair-wise iterative interactions, the population reaches a consensus state asymptotically. In this…
We consider multi-player games played on graphs, in which the players aim at fulfilling their own (not necessarily antagonistic) objectives. In the spirit of evolutionary game theory, we suppose that the players have the right to repeatedly…
We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
A special sorting operation called Context Directed Swap, and denoted \textbf{cds}, performs certain types of block interchanges on permutations. When a permutation is sortable by \textbf{cds}, then \textbf{cds} sorts it using the fewest…
We consider a scenario in which two reinforcement learning agents repeatedly play a matrix game against each other and update their parameters after each round. The agents' decision-making is transparent to each other, which allows each…
Cryptic crossword clues are challenging cognitive tasks, for which new test sets are released on a daily basis by multiple international newspapers. Each cryptic clue contains both the definition of the answer to be placed in the crossword…
Repeated interaction between individuals is the main mechanism for maintaining cooperation in social dilemma situations. Variants of tit-for-tat (repeating the previous action of the opponent) and the win-stay lose-shift strategy are known…
Several variations of hat guessing games have been popularly discussed in recreational mathematics. In a typical hat guessing game, after initially coordinating a strategy, each of $n$ players is assigned a hat from a given color set.…
In Stackelberg security games when information about the attacker's payoffs is uncertain, algorithms have been proposed to learn the optimal defender commitment by interacting with the attacker and observing their best responses. In this…