President Trump’s “Uncooperative Games”


19 Jul 2018


The trade war between the United States and most of its trading partners, China in particular, is reminiscent of John Forbes Nash’s “uncooperative games”. A mathematician whose career was impacted by schizophrenia, Nash worked on “Game Theory and Outcome”, particularly in relation to the implications resulting from individual optimization of choice. Now known as the Nash Equilibrium, it reflects a troubling situation, which shares some similarities to the Sino-US game currently playing out today.

Imagine a simple game played by two players. Each of the two can only choose black or white without consultation with the opponent. Four configurations are possible:

• A and B play white, they each win 50 euros.

• A plays white, B plays black, A wins nothing, B wins 100 euros.

• A plays black, B plays white, A wins 100 euros, B wins nothing.

• A and B play black: both players lose.

If the first player has a lot of confidence in the human spirit, he will play white on the assumption that B will do the same, if so A and B will both win 50 euros. If they continue with this strategy, the game is very profitable for both players, winning 50 euros each turn.

On the contrary, if A is suspicious, he will play black, and if B shares this scepticism, he also plays black, meaning that the game can last a very long time without any gains for either player. The player who chooses white runs the risk of improving his opponent’s situation at his own expense. Until this time however, the players are in a balance, a curious balance which ultimately produces the worst returns both collective and individually.

Replace A and B with the names of the Chinese and American presidents, whilst black represents a tax on a basket of goods, and you have a pretty good representation of what is happening today. Was it necessary to “wake up” Nash to come to the conclusion that the American president is engaged in a non-cooperative game? Probably not, the “uncooperative” characteristics seem to naturally apply to Donald Trump’s attitude.

The comparison with Game Theory deserves to be explored further. Unless both players are content to accept that they will never get rich (with the only consolation being that they will not be any worse off than their opponent), players A and B could consider a “better” strategy, different than one that ultimately leads to the previously described Nash Equilibrium being reached. One of these strategies is to play as your opponent did on the previous move. If B played white, the next move A plays white, if B played black, A will play black. By mirroring the opponent’s previous turn, the player sends a signal, allowing for the possibility of exiting the destructive sequence.

We reward the collaborative approach with a white, whilst we punish the selfish choice with black. This is what Xi Jinping has done since the beginning of the escalating tensions. He responds to every commercial attack with an announcement of the same type: he plays black. In the opposite camp the same is true, with the latest threat being the taxation of 200 billions worth of goods.

The negative characteristic of the Nash Equilibrium, typified by the adoption of an ongoing aggressive stance eventually always shows up, even in terms of the most stubborn player. If it is election time for one of the players, the period of stubbornness may be prolonged, nevertheless it will end.

As such we should take some comfort from this fact during the current period of trade confrontation between the United States and the rest of the world, the Nash Equilibrium is not inevitable. The Chinese market has dropped 10% since the start of the Sino-US verbal jousts, the yuan has dropped 5%, there has been a build-up in the moment waiting for one of the players to play white.



Marc is a Non Executive Director of the EI Sturdza Funds plc and former CIO and Member of the Executive Committee of La Financière De L’Echiquier.

Marc is an industry heavyweight and has extensive experience within industry, having held senior positions at Finacor, EBPF, LFDE and finally at La Financière De L’Echiquier (LFDE) since 1986. Marc joined LFDE in 2001 and was named CIO in 2009 taking charge of the investment team, with EUR 8.5 billion under management, investing in both the equity and fixed income (corporate and convertible) markets.

Marc oversaw the Investment process and provided top down macro guidance, as well as being responsible for the implementation of new tools and the expansion of LFDE’s product range. Marc was awarded the 2016 CIO of the year by “l’AGEFI” before leaving LFDE in October 2017 to pursue other passions.

The views and statements contained herein are those of the Marc Craquelin, Non Executive Director of EI Sturdza Funds plc as of 19/07/18.