The lottery Blotto game

Osório, António

doi:10.1016/j.econlet.2013.04.012

Cited by 26 publications

(9 citation statements)

References 7 publications

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“…More recently, Duffy and Matros (2015) extended the results of Lake (1979) for the case of asymmetric budgets, and the results of Friedman (1958) for more than two players. Osorio (2013) generalized the closed form solution from Friedman (1958) to the case of asymmetric players' valuations where candidates maximize the expected number of votes. Eiselt and Marianov (2020) frames the problem studied by Friedman (1958) in a leader-follower setting.…”

Section: Literature Reviewmentioning

confidence: 99%

On the Resource Allocation for Political Campaigns

Morales

Thraves

2021

Production and Operations Management

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I n an election campaign, candidates must decide how to optimally allocate their efforts/resources optimally among the regions of a country. As a result, the outcome of the election will depend on the players' strategies and the voters' preferences. In this work, we present a zero-sum game where two candidates decide how to invest a fixed resource in a set of regions, while considering their sizes and biases. We explore the two voting systems, the Majority System (MS) and the Electoral College (EC). We prove equilibrium existence and uniqueness under MS in a deterministic model; in addition, their closed form expressions are provided when fixing the subset of regions and relaxing the non-negative investing constraint. For the stochastic case, we use Monte Carlo simulations to compute the players' payoffs. For the EC, given the lack of equilibrium in pure strategies, we propose an iterative algorithm to find equilibrium in mixed strategies in a subset of the simplex lattice. We illustrate numerical instances under both election systems, and contrast players' equilibrium strategies. We show that polarization induces candidates to focus on larger regions with negative biases under MS, whereas candidates concentrate on swing states under EC. Finally, we calibrate the analyzed models with real data from the US 2020 presidential election.

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Section: Literature Reviewmentioning

confidence: 99%

On the Resource Allocation for Political Campaigns

Morales

Thraves

2021

Production and Operations Management

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“…More recently, Duffy and Matros (2015) extended the results of Lake (1979) for the case of asymmetric budgets, and the results of Friedman (1958) for more than two players. Osorio (2013) generalized the closed form solution from Friedman (1958) to the case of asymmetric players' valuations where candidates maximize the expected number of votes. Our work differs from these in the following aspects: (i) we incorporate states' biases, (ii) we allow for a more general representation of the stochastic voting outcome of each state (by using a Dirichlet distribution instead of a Bernoulli), and (iii) we explore equilibrium in mixed strategies.…”

Section: Looked Into the Electoralmentioning

confidence: 99%

On the Resource Allocation for Political Campaigns

Morales¹,

Thraves²

2020

Preprint

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In an election campaign, candidates must decide how to optimally allocate their efforts/resources optimally among the regions of a country. As a result, the outcome of the election will depend on the players' strategies and the voters' preferences. In this work, we present a zero-sum game where two candidates decide how to invest a fixed resource in a set of regions, while considering their sizes and biases. We explore the Majority System (MS) as well as the Electoral College (EC) voting systems. We prove equilibrium existence and uniqueness under MS in a deterministic model; in addition, their closed form expressions are provided when fixing the subset of regions and relaxing the non-negative investing constraint. For the stochastic case, we use Monte Carlo simulations to compute the players' payoffs, together with its gradient and hessian. For the EC, given the lack of Equilibrium in pure strategies, we propose an iterative algorithm to find Equilibrium in mixed strategies in a subset of the simplex lattice. We illustrate numerical instances under both election systems, and contrast players' equilibrium strategies. Finally, we show that polarization induces candidates to focus on larger regions with negative biases under MS, whereas candidates concentrate on swing states under EC.

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“…The I-system in the present paper is related with the literature on the Colonel Blotto game in which two budget constrained individuals allocate resources over a …nite number of issues (see Kovenock and Roberson (2012) for a survey of the multiple variations of the original problem). The main di¤erence between our approach and the Colonel Blotto game is that individuals are not budget constrained and the outcome of each issue is modeled with a Tullock's (1980) type CSF (Friedman, 1958;Snyder, 1989;Osório, 2013;Robson, 2005).…”

Section: Literature Reviewmentioning

confidence: 99%

Conflict and Competition over Multi-Issues

Osório¹

2018

The B.E. Journal of Theoretical Economics

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Real life disputes, negotiations and competitive situations involve multi-issue considerations in which the …nal outcome depends on the aggregated e¤ort over several dimensions. We consider two allocation systems, the I-system, in which each issue is disputed and award independently, and the A-system, in which all issues are aggregate in a single prize award. In the A-system, we propose a contest success function that aggregates the individuals' multi-issue e¤orts in a single outcome. Among other results, we found that the A-system tends to induce higher total e¤ort than the I-system.The model is also able to reproduce a large set of strategic behaviors. For instance, under decreasing returns to e¤ort, individuals maximize their payo¤s by distributing e¤ort over all issues, while under increasing returns to e¤ort, individuals focus on a single issue. Hybrid equilibria, in which one individual focus in a single issue while the other individual diversi…es e¤ort over all issues, may also emerge when individuals hold di¤erent returns to e¤ort. Strategic behavior is simultaneously in ‡uenced by the weight of each issue on the …nal outcome and by comparative advantages. Throughout the manuscript, we link our results with strategic behavior observed in electoral competition, i.e., "issue ownership", "issue divergence/convergence" and "common value issues". We expect that our …ndings will help researchers and practitioners to better understand the process of endogenous selection of issues in competitive contexts and to provide guidance in the implementation of the optimal allocation mechanism. JEL: C72, D72, D74, D81.

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The lottery Blotto game

Cited by 26 publications

References 7 publications

On the Resource Allocation for Political Campaigns

On the Resource Allocation for Political Campaigns

On the Resource Allocation for Political Campaigns

Conflict and Competition over Multi-Issues

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