相关论文: The standard deviation effect (or why one should s…
Adaptive populations such as those in financial markets and distributed control can be modeled by the Minority Game. We consider how their dynamics depends on the agents' initial preferences of strategies, when the agents use linear or…
Left-handedness is known to provide an intrinsic and tactical advantage at top level in many sports involving interactive contests. Again, most of the renowned leaders of the world are known to have been left-handed. Leadership plays an…
The 21-card trick is a way of dealing cards in order to predict the card selected by a volunteer. We give a mathematical explanation of why the well-known 21-card trick works using a simple linear discrete function. The function has a…
This work investigates continuous time stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. The control processes are…
Finding a counterfeit coin with the different weight from a set of visually identical coin using a balance, usually a two-armed balance, known as the balance question, is an intersting and inspiring question. Its variants involve…
In the best choice problem with random arrivals, an unknown number $n$ of rankable items arrive at times sampled from the uniform distribution. As is well known, a real-time player can ensure stopping at the overall best item with…
Recent studies on fairness in automated decision making systems have both investigated the potential future impact of these decisions on the population at large, and emphasized that imposing ''typical'' fairness constraints such as…
Benford's law is the statement that in many real-world data sets, the probability of having digit \(d\) in base \(B\), where \(1 \leq d \leq B\), as the first digit is \(\log_{B}\left(\tfrac{d+1}{d}\right)\). We sometimes refer to this as…
We argue that a restriction determined by a drawn card or quantum random numbers, on the running of LHC (Large Hadron Collider), which was proposed in earlier articles by us, can only result in an, at first, apparent success whatever the…
In competitive games with private objectives, actions can reveal information about hidden parameters. Quantifying such information revelation, however, is substantially more challenging, since it depends not only on the opponent's hidden…
There is a widespread notion in cricketing world that with increasing pace the performance of a bowler improves. Additionally, many commentators believe lower order batters to be more vulnerable to pace. The present study puts these two…
Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…
We study the asymptotic behavior of the ratio of total return (or total profit) to total amount bet in a casino game. While the limit is well understood when the sequence of wagers is independent and identically distributed, here we…
We consider a mean-field model for large banking systems, which takes into account default and recovery of the institutions. Building on models used for groups of interacting neurons, we first study a McKean-Vlasov dynamics and its…
In this article, we establish precise convergence rates of a general class of $N$-Player Stackelberg games to their mean field limits, which allows the response time delay of information, empirical distribution based interactions, and the…
Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth.…
Testing by betting has been a cornerstone of the game-theoretic statistics literature. One bets against the null hypothesis, and the accumulated wealth $W_t$ quantifies the evidence against the null hypothesis after $t$ rounds, and the null…
In a recent work Conger and Howald derived asymptotic formulas for the randomness, after shuffling, of decks with repeating cards or all-distinct decks dealt into hands. In the latter case the deck does not need to be fully randomized: the…
For scientific computations on a digital computer the set of real number is usually approximated by a finite set F of "floating-point" numbers. We compare the numerical accuracy possible with difference choices of F having approximately the…
We put forward a new model of congestion games where agents have uncertainty over the routes used by other agents. We take a non-probabilistic approach, assuming that each agent knows that the number of agents using an edge is within a…