Geopolitical Conflict Through the Lens of Nash Equilibrium

Before beginning this blog, I should acknowledge that I do not have the ability to speak with complete confidence about the current confrontation between the U.S. and Iran (March 2026). Those who are not direct participants in the conflict cannot fully understand the deeper motives, internal calculations, and hidden tensions between the parties. For that reason, as an outside observer, I am not in a position to make definitive judgments, since much of the true structure of the conflict is neither visible nor easily knowable.

Most media reports portray the current confrontation between the U.S. and Iran as a struggle between good and evil, or as the product of the greed of a few actors. While this framing attracts attention, it is analytically weak. Consequently, individual investors influenced by such narratives may misinterpret the prospects for war and make costly financial decisions. A recurring reality is that individual investors who simply follow sensational news headlines often underperform. Markets do not price moral stories; rather, they price incentives, constraints, probabilities, and strategic responses.

A more useful framework is Nash Equilibrium. In strategic conflict, each side chooses actions while anticipating the reactions of the other side. Outcomes are not determined by virtue or emotion alone, but by whether any player can improve its position by unilaterally changing strategy. Formally, if the United States chooses strategy $s_U$ and Iran chooses strategy $s_I$, with payoff functions $U_U(s_U,s_I)$ and $U_I(s_U,s_I)$, an equilibrium $(s_U^*,s_I^*)$ satisfies $U_U(s_U^*,s_I^*) \geq U_U(s_U,s_I^*)$ for all $s_U$, and $U_I(s_U^*,s_I^*) \geq U_I(s_U^*,s_I)$ for all $s_I$.

That means neither side can improve its position by changing strategy alone once the other side's choice is fixed. This matters because the United States and Iran are not making decisions in isolation. Each move---military signaling, sanctions, retaliation, diplomacy, proxy activation, or restraint---is chosen under expectations about the opponent's next move.

From that perspective, I believe both sides largely understood the likely final outcome of the negotiations---perhaps with greater than 90% confidence---and each attempted to extract incremental gains through limited tactical adjustments. A key asymmetry in preferences should also be noted: while one side tends to place greater emphasis on avoiding future risks, the other gives more weight to present conditions. A more realistic model must therefore include noisy and nonlinear factors, especially on the Iranian side, because power is distributed across multiple institutions and factions: elected offices, clerical authority, security organs, economic networks, ideological hardliners, pragmatists, and regional proxy relationships. We may write Iran's effective payoff as $\tilde{U}_I(s_U,s_I)=U_I(s_U,s_I)+\epsilon \Phi(s_U,s_I,\theta)$, where $\epsilon$ measures the scale of political noise, $\theta$ represents hidden internal factional variables, and $\Phi$ captures nonlinear interactions among competing institutions, ideological blocs, security networks, and proxy relationships. 

It is a repeated strategic game played under uncertainty, domestic fragmentation, and incomplete information. That may be less dramatic than television narratives, but it is far more useful for forecasting markets. In the negotiation stage (April 2026), the gap between the two sides may have narrowed in most areas—narrow enough to justify continued talks—though some differences still remain. At times, the main obstacle is not only the size of the gap itself, but also the inability of both sides to announce a deal confidently because of unresolved political, strategic, and domestic constraints.

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