Territorial Disputes in the Americas blog series. Post 21: Symmetric Nash Equilibrium (SNE), game theory and international territorial disputes

 

Symmetric Nash Equilibrium (SNE), game theory and international territorial disputes

To apply Symmetric Nash Equilibrium (SNE) in an n-player game theory context to the Falklands/Malvinas conflict, we need to conceptualize the situation where each player (Argentina, the UK, and the Falkland/Malvinas Islanders) aims to optimize their strategy given the strategies of others, assuming symmetry in the game’s structure.

In this context, “symmetry” implies that all players have identical strategy sets and payoff functions when roles are considered interchangeable. However, in this real-world scenario, this post will interpret symmetry more loosely to mean that each player’s payoff depends on the actions of all others in a balanced manner:

Setting Up the Game:

• Players: Argentina (A), United Kingdom (UK), and Falkland Islanders (FI).
• Strategies:
  • A: {Invade, Negotiate}
  • UK: {Defend, Concede}
  • FI: {Support UK, Seek Neutrality}
• Payoffs: These would be hypothetical and based on historical outcomes, political, economic, and social considerations:
• A Invades vs. UK Defends: High cost for both, potential loss of international standing for A, but national pride might be seen as a gain. FI would face significant upheaval.
• A Invades vs. UK Concedes: A gains territory but at the cost of international relations; UK loses prestige and territory; FI loses sovereignty.
• A Negotiates vs. UK Defends: No immediate conflict, but tensions remain; FI’s status quo preserved.
• A Negotiates vs. UK Concedes: Peaceful transfer of sovereignty might occur, A gains without war, UK avoids conflict but loses territory; FI’s preference depends on their alignment with UK or desire for self-determination.
• FI Supports UK: Enhances UK’s resolve, potentially escalates conflict; reduces A’s chance of success.
• FI Seeks Neutrality: Might reduce conflict intensity but leaves FI’s future uncertain.

Symmetric Nash Equilibrium Analysis:

• Equilibrium with Conflict: If both A and UK anticipate the other will act aggressively (Invade/Defend), no player can unilaterally change strategy for better outcomes. In this case, the equilibrium might involve:
  • A choosing “Invade” because defending the claim on the islands is seen as non-negotiable.
  • UK choosing “Defend” due to the high value placed on sovereignty and national pride, despite the costs.
  • FI choosing “Support UK” for maintaining status quo, leading to an equilibrium where conflict is likely.
• Equilibrium with Peace: Conversely, if all players recognize the high mutual costs of war:
  • A might choose “Negotiate” if the potential gains from peace (economic relations, international standing) outweigh the symbolic gain of the islands.
  • UK might choose “Concede” if the cost of conflict and maintaining the islands outweighs the benefits, especially if it’s seen as a diplomatic solution rather than a loss.
  • FI might “Seek Neutrality” if they believe their interests are better served by not escalating tensions, hoping for a diplomatic resolution where their rights are considered.
• Mixed Strategies: In reality, players might not commit fully to one strategy but play mixed strategies:
• A might mix between “Invade” and “Negotiate” to keep UK guessing, reducing the effectiveness of defense preparations.
• UK might similarly mix “Defend” with “Concede” to signal both resolve and openness to diplomacy.
• FI could alternate between supporting and neutrality to maximize influence in negotiations.

In a Symmetric Nash Equilibrium, each player’s best response to the strategies of others can lead to either conflict or peace. The equilibrium with conflict reflects the 1982 scenario where each side’s actions were predicated on the other’s expected behavior.

Post-conflict, a shift towards negotiation might reflect a new equilibrium where the costs of war are acknowledged, and peace through diplomacy becomes the best mutual strategy.

Obviously, it is important to note, this analysis simplifies a complex geopolitical situation into a theoretical model, where real-world variables like international law, domestic politics, and historical grievances significantly influence outcomes beyond pure game theory predictions. Other elements and factors such as leaders’ prestige, regional and international situation and questions pertaining to other cases such as Antarctica would need to be taken into account.

NOTE:

This blog series introduces, explains and assesses issues pertaining territorial disputes in the Americas including law, politics, culture, history and religion. There will be new posts every Monday, Wednesday and Friday.

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