# Abstract

Real life disputes, negotiations and competitive situations involve multi-issue considerations in which the final outcome depends on the aggregated effort 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 efforts in a single outcome. Among other results, we found that the A-system tends to induce higher total effort than the I-system. The model is also able to reproduce a large set of strategic behaviors. For instance, under decreasing returns to effort, individuals maximize their payoffs by distributing effort over all issues, while under increasing returns to effort, individuals focus on a single issue. Hybrid equilibria, in which one individual focus in a single issue while the other individual diversifies effort over all issues, may also emerge when individuals hold different returns to effort. Strategic behavior is simultaneously influenced by the weight of each issue on the final 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 findings 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.

## A Appendix

In the main text of this paper, in order to simplify the analysis and to provide better intuition, we have focused in the two individuals and two issues case. In this Appendix, we briefly consider the general model with an arbitrary number of issues. In this context, we should introduce extra notation to distinguish between individuals and issues.

### A.1 The general model

Let

In this context, under the multi-issue

with

Under the multi-issue

subject to the participation constraint

In order to have a sufficiently tractable

### A.2 General results and proofs

In the case

### Proposition 9.

*For**the individuals**equilibrium efforts in each issue**are given by*:

*where*

*and*

*with*

*for*

*and*

### Proof

[Proof of Proposition 10 (and Propositions 3 and 4)] The proof of Proposition 3 is just a particular case of this proof. From the problem 16, the associated set of

for

for

and, then summing over all issues

then,

for

**The proof of Proposition 4** is just a particular case of the following more general proof. Since in equilibrium each individual provides the same aggregate effort, i.e.,

is strictly positive if

In the case

### Proposition 10.

*For*

*the individuals equilibrium efforts in each issue**are given by*:

*where*

*and*

*for*

**Proof of Proposition 11 (and Proposition 5)**. The proof of Proposition 5 is just a particular case of this proof. Note that for

for ^{[13]} The individual

which is negative if

# Acknowledgements

Financial support from the Barcelona Graduate School of Economics and Univ. Rovira i Virgili are gratefully acknowledged. I would like to thank Matthias Dahm, Sabine Flamand, David Pérez-Castrillo, Ricardo Ribeiro and Santiago Sanchez-Pages as well as several seminars and congresses participants for helpful comments and discussions. All remaining errors are mine.

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**Published Online:**2018-01-20

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