Related papers: BONUS! Maximizing Surprise
We study a fair division problem with indivisible items, namely the computation of maximin share allocations. Given a set of $n$ players, the maximin share of a single player is the best she can guarantee to herself, if she would partition…
A knockout tournament is one of the most simple and popular forms of competition. Here, we are given a binary tournament tree where all leaves are labeled with seed position names. The players participating in the tournament are assigned to…
We study how individuals trade off outcome ("what") and process ("how") utility in high-stakes strategic decisions, namely professional tennis. Using optimality conditions and the second-service rule, we derive a sufficient condition for…
Game theory has been increasingly applied in settings where the game is not known outright, but has to be estimated by sampling. For example, meta-games that arise in multi-agent evaluation can only be accessed by running a succession of…
We study the classic divide-and-choose method for equitably allocating divisible goods between two players who are rational, self-interested Bayesian agents. The players have additive values for the goods. The prior distributions on those…
In this work the properties of multi choice minority games are studied by means of extensive computational simulations. We have considered several ways of rewarding the strategies of the players and compared the resulting behaviours of the…
Existing match classification models in the tournament design literature have two major limitations: a contestant is considered indifferent only if uncertain future results do never affect its prize, and competitive matches are not…
Consider a game consisting of independent turns with even money payoffs in which the player wins with a fixed probability $p \geq 1/3$ and loses with probability $1 - p$. The Labouchere system is a betting strategy which entails keeping a…
Rating systems play an important role in competitive sports and games. They provide a measure of player skill, which incentivizes competitive performances and enables balanced match-ups. In this paper, we present a novel Bayesian rating…
We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least…
Cooperative game theory has diverse applications in contemporary artificial intelligence, including domains like interpretable machine learning, resource allocation, and collaborative decision-making. However, specifying a cooperative game…
Behavioral experiments on the Ultimatum Game have shown that we human beings have remarkable preference in fair play, contradicting the predictions by the game theory. Most of the existing models seeking for explanations, however, strictly…
In many competitive settings, from education to politics, rules do not reward effort evenly, and thresholds (e.g., grade cutoffs or electoral majorities) make some moments disproportionately important. Success thus depends on efficiently…
We study the voting problem with two alternatives where voters' preferences depend on a not-directly-observable state variable. While equilibria in the one-round voting mechanisms lead to a good decision, they are usually hard to compute…
This work studies external regret in sequential prediction games with both positive and negative payoffs. External regret measures the difference between the payoff obtained by the forecasting strategy and the payoff of the best action. In…
We introduce and analyze a natural game formulated as follows. In this one-person game, the player is given a random permutation $A=(a_1,\dots, a_n)$ of a multiset $M$ of $n$ reals that sum up to $0$, where each of the $n!$ permutation…
Models in which the number of goals scored by a team in a soccer match follow a Poisson distribution, or a closely related one, have been widely discussed. We here consider a soccer match as an experiment to assess which of two teams is…
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.…
We study tournaments where winning a rank-dependent prize requires passing a minimum performance standard. We show that, for any prize allocation, the optimal standard is always at a mode of performance that is weakly higher than the global…
Corresponding to $n$ independent non-negative random variables $X_1,...,X_n$, are values $M_1,...,M_n$, where each $M_i$ is the expected value of the maximum of $n$ independent copies of $X_i$. We obtain an upper bound to the expected value…