824 research outputs found
One for all, all for one---von Neumann, Wald, Rawls, and Pareto
Applications of the maximin criterion extend beyond economics to statistics,
computer science, politics, and operations research. However, the maximin
criterion---be it von Neumann's, Wald's, or Rawls'---draws fierce criticism due
to its extremely pessimistic stance. I propose a novel concept, dubbed the
optimin criterion, which is based on (Pareto) optimizing the worst-case payoffs
of tacit agreements. The optimin criterion generalizes and unifies results in
various fields: It not only coincides with (i) Wald's statistical
decision-making criterion when Nature is antagonistic, (ii) the core in
cooperative games when the core is nonempty, though it exists even if the core
is empty, but it also generalizes (iii) Nash equilibrium in -person
constant-sum games, (iv) stable matchings in matching models, and (v)
competitive equilibrium in the Arrow-Debreu economy. Moreover, every Nash
equilibrium satisfies the optimin criterion in an auxiliary game
Optimin achieves super-Nash performance
Since the 1990s, AI systems have achieved superhuman performance in major
zero-sum games where "winning" has an unambiguous definition. However, most
social interactions are mixed-motive games, where measuring the performance of
AI systems is a non-trivial task. In this paper, I propose a novel benchmark
called super-Nash performance to assess the performance of AI systems in
mixed-motive settings. I show that a solution concept called optimin achieves
super-Nash performance in every n-person game, i.e., for every Nash equilibrium
there exists an optimin where every player not only receives but also
guarantees super-Nash payoffs even if the others deviate unilaterally and
profitably from the optimin.Comment: arXiv admin note: substantial text overlap with arXiv:1912.0021
Mutual knowledge of rationality and correct beliefs in -person games: An impossibility theorem
There are two well-known sufficient conditions for Nash equilibrium: common
knowledge of rationality, and common prior, which exogenously assumes a profile
of beliefs that are correct. However, it is not known how players arrive at a
common prior \textit{before} playing the original game. In this note, I assume,
in addition to (objective and subjective) rationality, that players' beliefs
\textit{will be} correct once the game is played, but a common prior is not
assumed. I study whether and under what conditions players endogenously arrive
at a common prior. The main finding is an impossibility theorem, which states
that mutual knowledge of rationality and mutual knowledge of correct beliefs
are not in general logically consistent in -person games. However, the two
assumptions are consistent in two-player zero-sum games
Exploring the Constraints on Artificial General Intelligence: A Game-Theoretic No-Go Theorem
The emergence of increasingly sophisticated artificial intelligence (AI)
systems have sparked intense debate among researchers, policymakers, and the
public due to their potential to surpass human intelligence and capabilities in
all domains. In this paper, I propose a game-theoretic framework that captures
the strategic interactions between a human agent and a potential superhuman
machine agent. I identify four key assumptions: Strategic Unpredictability,
Access to Machine's Strategy, Rationality, and Superhuman Machine. The main
result of this paper is an impossibility theorem: these four assumptions are
inconsistent when taken together, but relaxing any one of them results in a
consistent set of assumptions. Two straightforward policy recommendations
follow: first, policymakers should control access to specific human data to
maintain Strategic Unpredictability; and second, they should grant select AI
researchers access to superhuman machine research to ensure Access to Machine's
Strategy holds. My analysis contributes to a better understanding of the
context that can shape the theoretical development of superhuman AI.Comment: 15 page
The strategy of conflict and cooperation
In this paper, I introduce (i) a novel and unified framework, called
cooperative extensive form games, for the study of strategic competition and
cooperation, which have been studied in specific contexts, and (ii) a novel
solution concept, called cooperative equilibrium system. I show that
non-cooperative extensive form games are a special case of cooperative
extensive form games, in which players can strategically cooperate (e.g., by
writing a possibly costly contract) or act non-cooperatively. To the best of my
knowledge, I propose the first solution to the long-standing open problem of
"strategic cooperation" first identified by von Neumann (1928). I have one main
result to report: I prove that cooperative equilibrium system always exists in
finite -person cooperative strategic games with possibly imperfect
information. The proof is constructive in the case of perfect information
games.Comment: 57 page
Proportional resource allocation in dynamic n-player Blotto games
In this note, we introduce a general model of dynamic n-player multi-battle Blotto contests in which asymmetric resources and non-homogeneous battlefield prizes are possible. Each player’s probability of winning the prize in a battlefield is governed by a ratio-form contest success function and players’ resource allocation on that battlefield. We show that there exists a pure subgame perfect equilibrium in which players allocate their resources in proportion to the battlefield prizes for every history. We also give a sufficient condition that if there are two players and the contest success function is of Tullock type, then the subgame perfect equilibrium is unique
Farsightedness in Games: Stabilizing Cooperation in International Conflict
We show that a cooperative outcome—one that is at least next-best for the players—is not a Nash equilibrium (NE) in 19 of the 57 2 x 2 strict ordinal conflict games (33%), including Prisoners’ Dilemma and Chicken. Auspiciously, in 16 of these games (84%), cooperative outcomes are nonmyopic equilibria (NMEs) when the players make farsighted calculations, based on backward induction; in the other three games, credible threats induce cooperation. More generally, in all finite normal-form games, if players’ preferences are strict, farsighted calculations stabilize at least one Pareto-optimal NME. We illustrate the choice of NMEs that are not NEs by two cases in international relations: (i) no first use of nuclear weapons, chosen by the protagonists in the 1962 Cuban missile crisis and since adopted by some nuclear powers; and (ii) the 2015 agreement between Iran, and a coalition of the United States and other countries, that has been abrogated by the United States but has forestalled Iran’s possible development of nuclear weapons
Fairer Chess: A Reversal of Two Opening Moves in Chess Creates Balance Between White and Black
Unlike tic-tac-toe or checkers, in which optimal play leads to a draw, it is not known whether optimal play in chess ends in a win for White, a win for Black, or a draw. But after White moves first in chess, if Black has a double move followed by a double move of White and then alternating play, play is more balanced because White does not always tie or lead in moves. Symbolically, Balanced Alternation gives the following move sequence: After White’s (W) initial move, first Black (B) and then White each have two moves in a row (BBWW), followed by the alternating sequence, beginning with W, which altogether can be written as WB/BW/WB/WB/WB… (the slashes separate alternating pairs of moves). Except for reversal of the 3rd and 4th moves from WB to BW, this is the standard chess sequence. Because Balanced Alternation lies between the standard sequence, which favors White, and a comparable sequence that favors Black, it is highly likely to produce a draw with optimal play, rendering chess fairer. This conclusion is supported by a computer analysis of chess openings and how they would play out under Balanced Alternation
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