Related papers: Direct Proofs of Order Independence
We provide proofs for the fact that certain orders have no descending chains and no antichains.
In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.
In this paper, we study nonzero-sum separable games, which are continuous games whose payoffs take a sum-of-products form. Included in this subclass are all finite games and polynomial games. We investigate the structure of equilibria in…
We show, assuming weak large cardinals, that in the context of games played in a proper class of moves, clopen determinacy is strictly weaker than open determinacy. The proof amounts to an analysis of a certain level of $L$ that exists…
Delegation allows an agent to request that another agent completes a task. In many situations the task may be delegated onwards, and this process can repeat until it is eventually, successfully or unsuccessfully, performed. We consider…
We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step,…
In this work we discuss a random Tug-of-War game in graphs where one of the players has the power to decide at each turn whether to play a round of classical random Tug-of-War, or let the other player choose the new game position in…
We investigate the notion of independence, which is at the basis of many, seemingly unrelated, properties of logic like Rational Monotony in non-monotonic logics, and interpolation theorems.
The rationalizability concept was introduced in \cite{Ber84} and \cite{Pea84} to assess what can be inferred by rational players in a non-cooperative game in the presence of common knowledge. However, this notion can be defined in a number…
Learning models do not in general imply that weakly dominated strategies are irrelevant or justify the related concept of "forward induction," because rational agents may use dominated strategies as experiments to learn how opponents play,…
The recent years have seen interest into the possibility for (classical as well as quantum) causal structures that, while remaining logically consistent, feature a cyclic causal order between events, opening intriguing possibilities for new…
Recently, in [K.R. Apt and S. Simon: Well-founded extensive games with perfect information, TARK21], we studied well-founded games, a natural extension of finite extensive games with perfect information in which all plays are finite. We…
We define the family of {\it locally path-bounded} digraphs, which is a class of infinite digraphs, and show that on this class it is relatively easy to compute an optimal strategy (winning or nonlosing); and realize a win, when possible,…
Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier)…
Many results on the convex order in the literature were stated for random variables with finite mean. For instance, a fundamental result in dependence modeling is that the sum of a pair of random random variables is upper bounded in convex…
Various decomposition of finite games have been proposed. The inner product of vectors plays a key role in the decomposition of finite games. This paper considers the effect of different inner products on the orthogonal decomposition of…
Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the players' strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces…
We investigate the transfinite game values arising in infinite chess, providing both upper and lower bounds on the supremum of these values---the omega one of chess---with two senses depending on whether one considers only finite positions…
Dynamic evidence logics are logics for reasoning about the evidence and evidence-based beliefs of agents in a dynamic environment. In this paper, we introduce a family of logics for reasoning about relational evidence: evidence that…
We introduce the class of pay or play games, which captures scenarios in which each decision maker is faced with a choice between two actions: one with a fixed payoff and an- other with a payoff dependent on others' selected actions. This…