Game theory students will remember Selten’s chainstore paradox. An incumbent chainstore with huge profit margins seeks to fend off a potential entrant. This is a sequential move game. In the first stage, an entrant decides whether to contest a market and enter. In the second stage, the incumbent chainstore decides whether to accommodate entry and sustain high monopoly prices at the expense of sharing the market with the entrant, or, whether to start a price war—both the entrant and the incumbent lose so that, with hindsight, entry is an unprofitable proposition.
The chainstore’s initial position is clear. Threatening a price war prior to the entrant contesting the market discourages entry and in doing so preserves the chainstore’s monopoly profit. Compare that with the chainstore’s position once the entrant has set up shop and entered the market. Suddenly, starting a price war seems fanciful and expensive. The chainstore’s profit is greater when accommodating the entrant and sharing the market. The chainstore paradox says that even though it is in the chainstore’s best interest to threaten a price war, the entrant should not expect the chainstore to follow through on their threat once entry has already taken place. The threat of starting a price war is empty, whatever discourse precedes the entrant’s move can safely be labelled cheap talk.
From Chainstores to State Murder
What does the chainstore paradox have to do with state-sanctioned murder? Consider two countries, governed by two regimes, where at least one of the two does not subscribe to the sanctity of human life. To avoid all nuances, call one regime evil and the other innocent. Like the entrant, the evil regime moves first. And much like the entrant in the chainstore paradox, the evil regime must consider the potential responses of the innocent regime before taking action. Yet rather than contemplating an ultimately benevolent action—contesting a market for consumers’ gain—it ponders what to do about its exiled enemies. If in their self-interest, this evil regime kills, possibly abroad.
The innocent regime will seek to thwart the evil regime from murdering within its borders. Many punitive measures can be threatened in response. The politer ones include cutting low-level diplomatic ties, freezing the evil regime’s foreign assets, or pursuing economic sanctions. Unfortunately, doing so inflicts both direct and strategic cost upon the people governed by the innocent regime. Direct, because punitive measures inevitably destroy economic welfare. Strategic, because punitive measures can only be issued so many times until all leverage over the evil regime is lost. The innocent regime’s second stage choice that follows the state-sanctioned murder is simple: Leave it up to the judicial branch of government to pursue the murderer? Or, in addition, recognize the evil regime’s authorship, and, in response, issue punitive measures.
The Reality of Empty Threats
Most readers would wish to live in a world where the innocent regime threatens punitive measures that are muscular enough to discourage the evil regime from killing abroad. The terrifying logic of the chainstore paradox dictates another reality. We may repeat, almost verbatim, the preceding lines: Even though it is in the innocent regime’s best interest to threaten punitive measures, the evil regime should not expect the innocent regime to follow through on their threat once the evil regime has carried out the murder. The threat of punitive measures is empty, whatever discourse precedes the evil regime’s action can safely be labelled cheap talk. This is, of course, perfectly in line with the German government’s non-reaction to the Tiergarten murder where, sadly, no state doctrine exists to suggest a strong response.
Last week’s political news added two new stages to Selten’s chainstore paradox, guised as a model about state-sanctioned murder. Stage one: the evil regime decides whether to murder its enemies abroad. Stage two: the innocent regime decides whether to pursue punitive measures against the evil state (in addition to the judicial branch of government pursuing the murder). Stage three: the evil regime decides whether to take innocent citizens hostage. Stage four: the innocent regime decides whether to seek a release of the innocent hostages (held captive by the evil regime) by releasing the convicted murderer. The ensuing subgame perfect equilibrium is sobering. Once the innocent regime’s inability to commit upfront to a given course of action has been established, there is no limit to it serving as the evil regime’s punching back.
The Problem with Short-Term Thinking
Game theorists have developed the theory of repeated games to show that in an infinite horizon context a player’s ability to commit can be restored via the threat of future retaliatory (and temporary) punishment. The trouble is: democratically elected governments fail to take the long view come election time. The chance of being voted out of office dominates any long-term strategic concern that could guide their decision-making in any other year. Future hostage negotiations or thwarting future state-sponsored murders will then not weigh heavy on their mind. Last week’s hostage exchange, widely praised as a model of wise statecraft by many in the voting public, provides anecdotal evidence of this sobering principle in action. To prevent future murders, an urgent re-evaluation of how to rebuild deterrence—while preserving democratic accountability—is necessary.
