arXiv subjects

Marcin Dziubiński

Publications and source records attributed to Marcin Dziubiński.

10 recordsLinked to original sources

arXiv2026

Convergence rates of random-order best-response dynamics in public good games on networks

We study convergence rates of random-order best-response dynamics in games on networks with linear best responses and strategic substitutes. Combining formal analysis with numerical simulations we identify phenomena that lead to slow convergence. One of the key such phenomena is convergence to stable strategy profiles in parts of the network neighboring sets of nodes which remain inactive until the dynamics is close to converging and then switch to activity, initiating convergence to profiles with a new set of active agents and possibly leading to another iteration of such behavior. We identify structural properties of graphs which make such phenomena more likely. These properties go beyond the spectrum of a graph, which we demonstrate analyzing convergence rates on co-spectral mates.

cs.GT↗

arXiv2025

Peer Selection with Friends and Enemies

A planner wants to select one agent out of n agents on the basis of a binary characteristic that is commonly known to all agents but is not observed by the planner. Any pair of agents can either be friends or enemies or impartials of each other. An individual's most preferred outcome is that she be selected. If she is not selected, then she would prefer that a friend be selected, and if neither she herself or a friend is selected, then she would prefer that an impartial agent be selected. Finally, her least preferred outcome is that an enemy be selected. The planner wants to design a dominant strategy incentive compatible mechanism in order to be able choose a desirable agent. We derive sufficient conditions for existence of efficient and DSIC mechanisms when the planner knows the bilateral relationships between agents. We also show that if the planner does not know these relationships, then there is no efficient and DSIC mechanism and we compare the relative efficiency of two ``second-best'' DSIC mechanisms. Finally, we obtain sharp characterization results when the network of friends and enemies satisfies structural balance.

econ.TH↗

arXiv2025

Non-symmetric discrete Colonel Blotto game

We study equilibrium strategies and the value of the asymmetric variant of the discrete Colonel Blotto game with $K \geq 2$ battlefields, $B \geq 1$ resources of the weaker player and $A > B$ resources of the stronger player. We derive equilibrium strategies and the formulas for the value of the game for the cases where the number of resources of the weaker player, $B$, is at least $2(\lceil A/K \rceil - 1)$ as well as for the cases where this number is at most $\lfloor A/K \rfloor$. In particular, we solve all the cases of the game which can be solved using the discrete General Lotto game of~\cite{Hart08}. We propose a constrained variant of the discrete General Lotto game and use it to derive equilibrium strategies in the discrete Colonel Blotto game, that go beyond the General Lotto solvable cases game.

econ.TH↗

arXiv2025

Strategic hiding and exploration in networks

We propose and study a model of strategic network design and exploration where the hider, subject to a budget constraint restricting the number of links, chooses a connected network and the location of an object. Meanwhile, the seeker, not observing the network and the location of the object, chooses a network exploration strategy starting at a fixed node in the network. The network exploration follows the expanding search paradigm of Alpern and Lidbetter (2013). We obtain a Nash equilibrium and characterize equilibrium payoffs in the case of linking budget allowing for trees only. We also give an upper bound on the expected number of steps needed to find the hider for the case where the linking budget allows for at most one cycle in the network.

econ.TH↗

arXiv2025

Interconnected Contests

We study a two-player model of conflict with multiple battlefields -- the novel element is that each of the players has their own network of spillovers so that resources allocated to one battle can be utilized in winning neighboring battles. There exists a unique equilibrium in which the relative probability of a player winning a battle is the product of the ratio of the centrality of the battlefield in the two respective competing networks and the ratio of the relative cost of efforts of the two players. We study the design of networks and characterize networks that maximize total efforts and maximize total utility. Finally, we characterize the equilibrium of a game in which players choose both networks and efforts in the battles.

econ.TH↗

arXiv2025

Improved Approximation Ratio for Strategyproof Facility Location on a Cycle

We study the problem of design of strategyproof in expectation (SP) mechanisms for facility location on a cycle, with the objective of minimizing the sum of costs of $n$ agents. We show that there exists an SP mechanism that attains an approximation ratio of $7/4$ with respect to the sum of costs of the agents, thus improving the best known upper bound of $2-2/n$ in the cases of $n \geq 5$. The mechanism obtaining the bound randomizes between two mechanisms known in the literature: the Random Dictator (RD) and the Proportional Circle Distance (PCD) mechanism of Meir (arXiv:1902.08070). To prove the result, we propose a cycle-cutting technique that allows for estimating the problem on a cycle by a problem on a line.

cs.GT↗

arXiv2024

Efficient Method for Finding Optimal Strategies in Chopstick Auctions with Uniform Objects Values

We propose an algorithm for computing Nash equilibria (NE) in a class of conflicts with multiple battlefields with uniform battlefield values and a non-linear aggregation function. By expanding the symmetrization idea of Hart [9], proposed for the Colonel Blotto game, to the wider class of symmetric conflicts with multiple battlefields, we reduce the number of strategies of the players by an exponential factor. We propose a clash matrix algorithm which allows for computing the payoffs in the symmetrized model in polynomial time. Combining symmetrization and clash matrix algorithm with the double oracle algorithm we obtain an algorithm for computing NE in the models in question that achieves a significant speed-up as compared to the standard, LP-based, approach. We also introduce a heuristic to further speed up the process. Overall, our approach offers an efficient and novel method for computing NE in a specific class of conflicts, with potential practical applications in various fields.

cs.GT↗

arXiv2023

Computation of Nash Equilibria of Attack and Defense Games on Networks

We consider the computation of a Nash equilibrium in attack and defense games on networks (Bloch et al. [1]). We prove that a Nash Equilibrium of the game can be computed in polynomial time with respect to the number of nodes in the network. We propose an algorithm that runs in O(n4) time with respect to the number of nodes of the network, n.

cs.GT↗

arXiv2023

Discrete Two Player All-Pay Auction with Complete Information

We study discrete two player all-pay auction with complete information. We provide full characterization of mixed strategy Nash equilibria and show that they constitute a subset of Nash equilibria of discrete General Lotto game. We show that equilibria are not unique in general but they are interchangeable. We also show that equilibrium payoffs are unique, unless valuation of at least one of the players is an even integer number. If equilibrium payoffs are not unique, continuum of equilibrium payoffs are possible. We compare equilibrium characterization and equilibrium payoffs with the continuous variant of all-pay auctions.

cs.GT↗

arXiv2018

Individual Security and Network Design with Malicious Nodes

Networks are beneficial to those being connected but can also be used as carriers of contagious hostile attacks. These attacks are often facilitated by exploiting corrupt network users. To protect against the attacks, users can resort to costly defense. The decentralized nature of such protection is known to be inefficient but the inefficiencies can be mitigated by a careful network design. Is network design still effective when not all users can be trusted? We propose a model of network design and defense with byzantine nodes to address this question. We study the optimal defended networks in the case of centralized defense and, for the case of decentralized defense, we show that the inefficiencies due to decentralization can be fully mitigated, despite the presence of the byzantine nodes.

cs.GT↗