Mathematical Social Sciences最新文献

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.

We consider an optimal growth model in which the decision maker chooses the consumption path that maximizes her utility over a finite planning horizon. At each instant of time, she can opt for a regular product that pollutes the environment, or a non-polluting frugal product, which procures, however, lower utility. Depending on the parameter values, different optimal paths can materialize, including some where a frugal lifestyle is on the rise, and others where polluting persists during the planning horizon.

In this note, we investigate the relationship between non-manipulability via merging (splitting) and strong non-manipulability via merging (splitting). Our analysis reveals that while these two non-manipulability axioms are generally not equivalent, they do coincide when the principle of solidarity is satisfied. This principle is fulfilled by a wide range of bankruptcy rules, including parametric rules.

In this paper, we introduce a weaker notion of separability for set-systems and demonstrate that the class of maximal weakly separated systems precisely corresponds to the class of peak-pit maximal Condorcet domains. Additionally, we present a generalisation of arrangements of pseudolines and establish that the sets of chamber sets from them coincide with maximal weakly separated systems, enabling the construction of all peak-pit maximal Condorcet domains. Furthermore, we reveal that peak-pit maximal Condorcet domains coincide with connected maximal Condorcet domains.

We provide an axiomatic foundation for a choice model with two periods between which preferences are updated, but the second period choices are positively correlated with past choices in a manner that is unrelated to the agent’s preferences. Specifically, in our model, the agent chooses alternative $x$ over alternative $y$ in contrast to his past choice if and only if the difference between the utility of $x$ and that of $y$ is higher than some fixed cost. While restrictive in its nature, this representation captures several related but distinctive phenomena: a taste for consistency, cognitive dissonance, the escalation of commitment, passive choice, and habit formation. We also provide a representation that allows for a more general form of cost and the revealed preference implications of our models. Finally, we connect our representation to the theories of imperfect discrimination.

We consider the fundamental problem of fairly allocating indivisible items when agents have strict ordinal preferences over individual items. We focus on the well-studied fairness criterion of necessary envy-freeness. For a constant number of agents, the computational complexity of the deciding whether there exists an allocation that satisfies necessary envy-freeness has been open for several years. We settle this question by showing that the problem is $\mathrm{NP}$-complete even for three agents. Considering that the problem is polynomial-time solvable for the case of two agents, we provide a clear understanding of the complexity of the problem with respect to the number of agents.

I apply persuasion to a linear-in-best-responses setup that encompasses Bertrand and Cournot Oligopolistic Competition games. Before the state of the world is realized, firms must design public signals regarding an individual payoff parameter. Full Disclosure enables companies to connect actions to states of the world at the expense of releasing crucial information to the competitors. On the other hand, Partial Revelation makes companies lose optimality of the decisions with regards to the state of the world but enable them to commit to an aggressive policy of preclusion that increases the frequency of a favorable distribution of players actions in the Cournot case; an informational entry deterrence mechanism. I show that linearity and the presence of interior solutions lead to Full Disclosure as a dominant strategy whereas obfuscation arises as an optimal policy when a firm has the capacity to take an opponent out of operation in the Cournot case.

We analyze the effect of targeted informative advertising on firms’ incentive to improve product quality and the welfare implications. We find that, compared with mass advertising, targeted advertising results in (i) a decreased incentive to invest in R&D unless the cost of advertising is sufficiently low, (ii) a lower mark-up, net of product quality, being charged to consumers, and (iii) a smaller (larger) proportion of uninformed consumers when the cost of advertising is low (high). The firms may earn higher or lower profits, but consumers are usually better off due both to the lower net mark-up and to improved product-consumer match. Under certain conditions though, the negative impact of more uninformed consumers dominates and leads to reduced consumer and total welfare.