Related papers: Solving the social choice problem under equality c…
Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice…
Evolutionary game theory assumes that individuals maximize their benefits when choosing strategies. However, an alternative perspective proposes that individuals seek to maximize the benefits of others. To explore the relationship between…
In its simplest form the well known consensus problem for a networked family of autonomous agents is to devise a set of protocols or update rules, one for each agent, which can enable all of the agents to adjust or tune their "agreement…
In many combinatorial problems one may need to model the diversity or similarity of assignments in a solution. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this…
For a binary choice problem, the spatial coordination of decisions in an agent community is investigated both analytically and by means of stochastic computer simulations. The individual decisions are based on different local information…
We study a simple example of a sequential game illustrating problems connected with making rational decisions that are universal for social sciences. The set of chooser's optimal decisions that manifest his preferences in case of a constant…
Consider a distribution of citizens in an urban area in which some services (supermarkets, post offices...) are present. Each citizen, in order to use a service, spends an amount of time which is due both to the travel time to the service…
A principal can restrict an agent's information (the persuasion problem) or restrict an agent's discretion (the delegation problem). We show that these problems are generally equivalent - solving one solves the other. We use tools from the…
We study a simple problem of allocating common-value goods. The designer seeks to allocate the goods to as many unit-demand agents as possible without monetary transfers, while agents, who possess partial private information about the…
We introduce a novel family of mechanisms for constrained allocation problems which we call local priority mechanisms. These mechanisms are parameterized by a function which assigns a set of agents, the local compromisers, to every…
Recently, group recommendations have attracted considerable attention. Rather than recommending items to individual users, group recommenders recommend items to groups of users. In this position paper, we introduce the problem of forming an…
During deliberation processes, mediators and facilitators typically need to select a small and representative set of opinions later used to produce digestible reports for stakeholders. In online deliberation platforms, algorithmic selection…
Many high-stakes AI deployments proceed only if every stakeholder deems the system acceptable relative to their own minimum standard. With randomization over a finite menu of options, this becomes a feasibility question: does there exist a…
We consider a moral hazard problem with multiple principals in a continuous-time model. The agent can only work exclusively for one principal at a given time, so faces an optimal switching problem. Using a randomized formulation, we manage…
It has been argued that one role of social constructs, such as institutions, trust and norms, is to coordinate the expectations of autonomous entities in order to resolve collective action situations (such as collective risk dilemmas)…
As the world's democratic institutions are challenged by dissatisfied citizens, political scientists and also computer scientists have proposed and analyzed various (innovative) methods to select representative bodies, a crucial task in…
In this paper an interesting application of mathematics in economics is presented: the formulation of the theory of consumer basic problem, grounded on the concept of preferences relation and operationalized with optimization tools.
People care about decision outcomes and how decisions get made, both when making decisions and reflecting on decisions. But formalizing the full range of normative concerns that drive decisions is an open challenge. We introduce Axiomatic…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
Given the family $P$ of all nonempty subsets of a set $U$ of alternatives, a choice over $U$ is a function $c \colon \Omega \to P$ such that $\Omega \subseteq P$ and $c(B) \subseteq B$ for all menus $B \in \Omega$. A choice is total if…