A Location Game On Disjoint Circles



the other so that a player wins if and only if the area it secures is strictly
the largest one. Otherwise there is a tie. It is shown in Ahn et al. [2004]
that in this game G always has a winning strategy, though R can bring its
length of influence as close as that of G’s. Our objective is to check if such
a second mover advantage prevails when there are more that one disjoint
identical circles. We now present these ideas and the finding in Ahn et al.
[2004] formally.

Let {R, G} be a set of players, where R stands for Red and G stands
for Green.
The game on the family of disjoint circles is defined by a pair
hN, {C
j}jK=1 i, such that N > K ≥ 1 and {Cj}jK=1 is a family of K disjoint
circles. Notice that the game studied in Ahn et al. [2004] is the special case
where K = 1. Throughout the game each player p
{R, G} will select a total
of N points on K circles. The set of points selected by R is Γ SjK=1 Cj
and the set of points selected by G is Ω SjK=1 Cj. Players re-arrive in
alternating sequence with R moving first, and are in principle allowed to
place points in batches. Let Γ
r be the set of points that R places in round
r ≥ 1 while Ω
r be the same for G. The game ends when all 2N points are
placed on the circles.
4 We will use w Γ (b Ω) to denote a point placed
by R (G) during the game. We will call points placed by the player R
red
points
and those placed by the player G green points.

As discussed above, the game has the following conditions:

1. Γr, Ωr ≥ 1 for every r ≥ 1.

2. Γι < N.

3. PrΓiprΩi for every r ≥ 1.

4 Please note that we put no restriction on how players distribute these points across
the circles (some circles are allowed to remain empty in which case it is ignored while
computing payoffs).



More intriguing information

1. The name is absent
2. Une Classe de Concepts
3. Estimation of marginal abatement costs for undesirable outputs in India's power generation sector: An output distance function approach.
4. The name is absent
5. Foreign Direct Investment and Unequal Regional Economic Growth in China
6. Endogenous Heterogeneity in Strategic Models: Symmetry-breaking via Strategic Substitutes and Nonconcavities
7. BEN CHOI & YANBING CHEN
8. The name is absent
9. The Mathematical Components of Engineering
10. Climate Policy under Sustainable Discounted Utilitarianism
11. Contribution of Economics to Design of Sustainable Cattle Breeding Programs in Eastern Africa: A Choice Experiment Approach
12. New urban settlements in Belarus: some trends and changes
13. The name is absent
14. Bird’s Eye View to Indonesian Mass Conflict Revisiting the Fact of Self-Organized Criticality
15. Testing Hypotheses in an I(2) Model with Applications to the Persistent Long Swings in the Dmk/$ Rate
16. Iconic memory or icon?
17. Experimental Evidence of Risk Aversion in Consumer Markets: The Case of Beef Tenderness
18. Hemmnisse für die Vernetzungen von Wissenschaft und Wirtschaft abbauen
19. Social Cohesion as a Real-life Phenomenon: Exploring the Validity of the Universalist and Particularist Perspectives
20. Publication of Foreign Exchange Statistics by the Central Bank of Chile