Posts Tagged ‘Economics & chess’

Playing the Spectator While Waiting for Covid

Across the world we are adjusting and adapting to life under lockdown, furloughed, cocooning, and moving around within an agreed social distance. We are responding to a new world order under Covid, a new normal with a greater degree of mutual interdependence as people observe and respond to each other’s behaviour. While there are computer games[1] to teach the importance of social distancing, we wondered whether or not game theory reasoning could underpin our behaviour during the Covid pandemic. The essay is about game theory reasoning and its putative relevance to rational behaviour under Covid. Related research into the aesthetics of game theory reasoning in literature inspired a reading of Sophocles’ Antigone and Beckett’s Waiting for Godot and Watt. The research[2] into obedience and waiting is ongoing but some thoughts are shared here as we design a game of obedience and waiting with a view to understanding of our own rational behaviour during this Covid pandemic. In these unsettling times, if one can only think of something as unbelievable as invisible Zen archers then there is hope in knowing that we are all facing this together.

Obedience as a Waiting Game

Sophocles’ play Antigone provides an historical canvas. The play is about pride and responsibility but, it is also a story about the rule of law, the role of Government and civil disobedience. Antigone is also[3] a ‘public story’, in terms of obeying a universal law. Should Antigone have adhered to the rule of law, the law of the State, and thus, obey her uncle King Creon? Or, choose not to obey. Like Antigone we have free will. Like Vladimir and Estragon we wait. So, do we adhere to the rules and obey Government guidelines, or do we disobey? The same reasoning would apply to groups and (economic) clubs[4] wherein members adhere to rules and regulations. Rational players as individuals do commit to an organised set of rules.

It has been shown by Schelling[5] that it is ‘not always safe to assume (individual) outcomes accurately express the individual decisions’ as observed.  Therefore in the search for rationality in a game of obedience, there may be a sub-game ‘trembling hand’ equilibrium in waiting, if we can interpret waiting as obedience. Our research has focused on an optimal design of a game of waiting inspired by a reading of Beckett’s Waiting for Godot and Watt. And suffice to note here in our design that the etymology of ‘waiting’ is either an interpretation of ‘hoping’ [Latin verb ‘spero’] as in Antigone’s behaviour, hoping to bury her dead brother or an interpretation ‘remaining in place’ [Latin verb ‘manere’] like Vladimir and Estragon as they wait for Godot. The latter interpretation is applied in this Blog essay. That is, we either obey Government restrictions and wait for further guidance or we disobey.

Ontological Insecurity

But there is an added poignancy to Sophocles’ narrative today during the Covid-19 pandemic as citizens in particular begin to question and debate Government policy. Covid-19 has disrupted individual and collective confidence. It has triggered what sociologists[6] and anthropologists[7] call ‘ontological insecurity’- an anxiety about your safety and security at a moment in time. We are now in a state of perpetual angst. It can be best understood by your answer to the question: how safe do you feel? We need assurance: in the medium term the roll-out of a track and tracing app or the wearing of masks might suffice. Masks or face coverings, for example, provide confidence and security: you wear a mask to protect others and they wear a mask to protect you from Covid infection. A vaccine would provide long term assurance. However, while it is sufficient to observe others taking precautions it is necessary for our own security that others, have confidence in their own survival. Therein lies the mutual interdependence that is characteristic of game theory.

Player Unknown

Like Antigone, we as citizens are now players in a game of obedience. The game is between you, Player 1, and ‘others’, referred to as Player Unknown (PU).[8] The PU allows us to blend the ontological insecurity of rational players into the game design. Antigone did not have to obey her uncle King Creon. She chose not to. Ultimately, like Antigone your playbook is a question of individual choice versus fate. There are many scenarios? What if King Creon did not expect Antigone to bury her brother Polynices? What if Estragon followed Pozzo and opted not to wait for Godot? We opted not to explore these hidden games with mixed strategies in this essay. They are to follow.

We ascribe Covid-19 behaviour as obedience and in an obedience game we have illustrated the payoff to ‘others’ in italics in Table 1 and the payoffs to you are illustrated in bold. Every player is unknown to you and you have zero information on any player. PU provides a cognitive framework that enables you, as a rational player, to anchor your confidence to observed behaviour by any PU. How would you choose your strategy of play in such a game? Players are rational and optimise their choices to get the most preferred outcome. PU would like to avoid the game or transfer responsibility to others. The sub-game payoffs reflect this preference ordering. Although the payoffs in Table 1 are arbitrary cardinal numbers, they do reflect the players’ preferences in a game of obedience. As citizens we have become players in a Covid obedience game. The ethical trade-off, arguably, do X and not Y is reminiscent of the narratives in Sophocles and Beckett. We opt to frame the trade-off as a non-cooperative game.

Trembling Hand Equilibrium

The trade-off is between individual choice and fate. We wait, we obey. Or not. It is a strategic choice with a sub-game perfect equilibrium. In other words,[9] obey as a strategy, is the Nash strategy in the ledger of choice for the duration of the game. Obedience, may well be the sub-game node to the main game of Covid survival over pride. The player’s payoffs take the cardinal form (-1, 0, 1, 2). The equilibrium payoff (2,1), for example, can best be understood by the philosophy[10] of Montaigne: ‘my life has been destroyed by many catastrophes most of which never happened’.

Table 1: Sub-game equilibrium with Player Unknown



Disobey 0, 1 0, 1
Obey 1, -1 2, 1


To obey the rule of law, to obey the Government until lockdown is eased and a vaccine available presents each and every one of us with a rational choice to obey. That choice is best understood by adapting the words of an old Biblical tenet[11] sic ‘I obey because it is absurd’. Playing this game with rational obedience in the playbook will obtain the payoff 2 for you as the rational player. Disobedience is not an option for you. There is no later. Every form of behaviour is shaped by trial and error. Disobedience, however, may obtain an elusive payoff of 1 for PU with an inherent risk of -1. For Antigone, it meant her death. What if she no longer believed in her strategy of disobedience?

Topology of a Playing Strategy

So let us consider two equilibria: the (2,1) payoff and a ‘hidden’ equilibrium[12]. The equilibria are separated by a probability (function) of reciprocal altruism[13]. The selfish outcome is present in both but due to a payoff equation (yet to be defined) it manifests itself differently in the two equilibria. Therefore the altruism function could be a discontinuity that can be developed from the differential form of the equation of life[14].

Definition: An equilibrium is hidden if it does not intersect with a well-defined open neighbourhood of equilibrium points. Or it may be a point in a small open neighbourhood whose closure is compact.

Theorem (to be proven): The (2,1) equilibrium payoff is a subset of a larger group of non-observant ‘hidden’ equilibria corresponding to a topological vector space wherein a convergence is defined in the neighborhood of saddle points.

Corollaries: I: The neighborhood of saddle points include a neighbourhood of 0. II: The vector space would include the payoffs at the default position of selfish behaviour by PU and the payoffs with co-evolution of the players who ascribe to a reciprocal altruism type.


Until further research is concluded, the payoff (2,1) is a trembling hand equilibrium. It can only occur if PU commits to obey as a strategy. So, ask yourself: should you obey? Affirmatively, yes. In a Bayesian game, Nature reports to each player his or her type. Are you Player Unknown? The equation of life in a Covid game is analogous to a Krepski two-move game of chess at a moment in time: opening move is either obey or disobey. If you disobey there is a greater risk of death. Checkmate. But this checkmate can only occur if one player (say, White in chess) commits to a mistake[15] so it seldom happens in practice. An anonymous rational PU in a two-move game does not want to die anonymously. If you obey the rules and guidance, you could evolve as a spectator to obedience, secure in the knowledge of your own survival and the survival of others. Despite disobedience by PU, behaviour will tend to cluster around (2,1) because there are many more rational players like you subject to the Gaussian distribution of rational behaviour. There is hope. The equilibrium point of balance in this stylised obedience game of waiting is realised when you can begin[16] to construct ceremonies out of the air and breathe upon them’. The Zen archers become visible. Keep safe. Keep sane.

[1] Check the Thomas Reuters Foundation article by Emma Batha, ‘Covid-19 Computer Games Reaches Children Importance of Social Distancing’, 19 May 2020

[2] Collaboration with Manfred Holler at LMU in Munich ‘waiting games’ inspired by the literature of Beckett and Brecht and the narratives in both Greek tragedy and Roman comedies, in Sophocles and Seneca respectively. The idea is a Beckett player type delaying and thinking [like the ‘sanyasin’ in Hindu] as observationally equivalent to waiting. Interesting perspective from Kimberley Bohman-Kalaja who published Playing the Spectator While Waiting for Godot at Princeton University Press, 2007.

[3] The view expressed originally by Holderlin who translated the play from Greek into German.

[4] McNutt, Patrick (2002): Economics of Public Choice Elgar Publishing, UK.

[5] Schelling’s Game Theory p241 by Robert Dodge (2012) Oxford University Press.

[6] Framed by Giddens (1990) in his book Modernity and Self Identity as ‘ontological security’ with the earlier original concept of insecurity attributable to R.D. Laing (1960): The Divided Self Penguin, London.

[7] Refer to the R.D.Laing’s research overlap with the grid-group analysis of Mary Douglas and Margaret Mead and application in an earlier article McNutt (1987): ‘Anthropology, Economics and the Socio-Economy’ The Arab Journal of the Social Sciences vol 2 no 1 April.

[8] Adapting the strategy from the gaming fraternity’s Player Unknown Battle Ground (PUBG): worksheets from my lecture notes ascribed to the MBA cohorts who attended Masterclass at both Manchester and Smurfit Business Schools in Manchester and Dublin.

[9] Check out McNutt (2010): Decoding Strategy published by McGrawHill and Holler (2018): The Economics of the Good, the Bad and the Ugly, Routledge.

[10] Selected from Montaigne’s Essais (1595) as translated in the essays in Wikisource.

[11] Adapted from an old Christian tenet ‘credo quia absurdum’ – ‘I believe because it is absurd.’

[12] The term suggested by colleague Manfred Holler at LMU and Hamburg.

[13] From McNutt (1988): ‘A Note on Altruism’ International Journal of Social Economics vol 15 pp62-64.

[14] The equation of life to be a diffusion like equation expressed in terms of the movement from selfish to altruistic behaviour in a Covid-type obedience game.

[15] The game design with a mixed strategy would assign probabilities to a second move for Antigone. What if she no longer believed in her strategy of challenging her uncle?

[16] Adapted from the narrative in Cormac McCarthy’s 2006 novel The Road at page 78 ‘where you have nothing else construct ceremonies out of the air and breathe upon them’.

An ultimatum game of ichi-go ichi-e

There was an opportunity, one meeting at Osaka for world leaders at the recent G20 summit. A valuable starting point for the policy-makers, faced with a menu of economic theories, is trust in each other and a new inter-disciplinary approach with an emphasis on ethics and economics. Climate change, migration and displacement, IoT and 5G, global income inequality, household mortgage debt, value of drinking water and food shortages present a grand ethical challenge. In 2015 we asked has economics become an illusion? An era of wistful economics:

Taylor Principle

This time, however, global economic policy should be less about money supply and demand, less about central banks modelling and the private sector and more about the strategic interaction between these ethical challenges.  There is an urgent need for coordinated action to stimulate the global economy with fiscal and monetary measures. The EU is fragmenting. Whither the Euro? Today, Federal debt is projected to jump to a record 144% of US GDP by 2049. There is a debt mountain in China reported at 250% debt-to-GDP. As the Scylla of the Taylor principle (of high interest rates when there is high inflation and low interest rates when unemployment is high) causes a modelling whirlpool with the Charybdis of the Ramsey approach to optimal monetary taxation, the appropriateness of an ethical fiscal policy as a stabilisation tool may calm the waters. So, more fiscal stimulus is required.


On a macro level, world politics is more about China’s transition to greater exchange rate flexibility and the internationalisation of the Chinese RMB. We had presented on this point in Shanghai in 2012. It’s a long game. In other words, RMB v US$ is an infinite game of playing the game not a finite game of first mover advantage. . A weaker RMB would probably mean a stronger US dollar and vice versa. We are reminded of Japan’s exit from its dollar peg in 1971 as today the game is one of reserve currency competition, whether or not the US dollar is destined to lose its standing as the preeminent international currency to Sterling, the Euro or the RMB. Trade wars, competitive devaluations, Brexit, military conflict create sudden disruptions to growth at a moment in time.

Productivity Bonus

As a countermove we become risk-averse on currency fluctuations. But there is a curved ball from the EU and the US regulators as their antitrust focus on big tech. Based on the presumption of a negative effect on competition it relies wholly on an attack on monopoly rents as a reward to innovators. Nonetheless, shareholders and investors and pension funds gain too. However, if the model builders could adapt the McKenzie model of classical general equilibrium theory so that technology is available to any company who can supply the resources required, ultimately, by happenstance, competition and innovation will coalesce into a productivity bonus. Big tech and technology could then be viewed as a way to escape classical monopoly by innovating to compete. To do so would require the equivalent of the 1919 Colgate doctrine for big tech, facilitating the introduction of new technology by allowing each of the big tech companies to decide, on its own, with whom to do business. They exercise discretion on innovation and technology; we, as onsumers,  decide. Our behaviour, after all, is less measured by prices, supply and demand but more influenced by small changes in innovation and technology over shorter time periods.

Onsumers & Complexity

Albeit, our policy advisers and central bankers are less likely to ever move away from the standard Ricardian DGSE models of economic analysis. There is a sunk cost to the modelling.  A key assumption in this model is that households like you and I are a homogeneous family of infinitely lived individuals. Really? This is 2019 and a more realistic and heuristic approach would address the fact that individual’s behaviour changes over shorter time periods with innovation and technology. Our well-ordered lives bring the occasional disturbance that can be characterized by an unmanageable degree of complexity. In our real world, we as onsumers, for example, shopping online, continue to bid against ourselves in the search for the best algorithmic deal.  In practical terms we do not behave as hyper-rational beings. At every G20 there is a risk-bucket and world leaders may get a chance to try again at another meeting; at this G20 there was one chance to try: ichi-go ichi-e. The ethical challenges of climate change, mortgage debt, migration and displacement, IoT and 5G, global income inequality, value of drinking water and food shortages all collapse into a generalized ultimatum game in which we as players must agree or we all get nothing.

Fiscal cliff and Kantian equilibrium

The fiscal cliff is the Nash Equilibrium [NE] is the best the Democrats can do given the reaction of the Republicans; they will debate big ticket items on spending asnd taxes but both know that neitherparty wants to go there  –  but it will happen if there is no compromise, according to game theory. The NE is often best understood as a ‘trap’ to avoid, but you can only avoid it, if there is compromise, and we can only compromise if I trust you and you trust me! The ethical dimension to this can be found in the answer to ‘who will compromise first’, that is, fulfil duty and take responsibility to find a Kantian equilibrium; the Kantian sequence could be observed….Move A:  I move first, then you follow: Move B: you move next and then I follow..Move C: we both observe each other as ‘taking responsibility’…How either party moves in the sequence and thus ‘fulfils duty’ depends on what each party believes the other will do…you might just be about to read these signals in the US.

Spin-0 for Apple in a French defence: from iPod to iNext or acquire a telco?

In our previous Blog entries, on the smartphone and tablet market, we referred to the market as a game, G. In G a new phenomenon has occurred, created by a convergence of technology coupled with rational consumers asking: is the iPhone5 = a mini iPad or is the new iPad mini = iPhone6? This line of questioning, we believe, translates the Apple products into a scalar (spin-0) with no strategic direction. A scalar product, if you recall from physics, only needs a numerical value, and is not attached to a direction. Where is Apple going? Earlier this year, IDC Research reported that Apple’s share of the global market for tablets fell sharply in 2012 from 65% to 50%.

Strategists therefore need to ask the entropy question: do gains necessarily accrue to Samsung, Amazon and Asus or are rational consumers simply waiting or delaying buying Apple devices? To find an answer, we posit that Apple products and non-Apple products may share common features and functionalities but they do not overlap, thus creating lines of adjacent vertices in an evolving market share game.  Furthermore, Apple may have the greatest App store in the game but as it continues to rotate through iPod, iPhone and iPad to iNext, spherical  competitors from anywhere at any time to will enter the game and win.  Rational consumers delaying a purchase and the convergence in rival technologies facilitate competition, and by Q4 2011 Google powered devices began to close in on Apple’s dominance. More recently, Microsoft’s Surface, the Google-Samsung Nexus 10 running on the latest Jelly Bean software, the Amazon Kindle Fire HD and the Asus-Google Nexus 7 have emerged as formidable competitors in the game.

What if the XBox music internet service has the potential to impact on iTunes? Investors are not clueless about the technology convergence nor are they aloof to the need for an optimal strategic response from Apple. With a cash balance that is equivalent to a quarter of its CAPM, investors will want more investment. They may ask: why not acquire a telco? The iPhone5 can indeed promise 4G technology, albeit not everyone, who has an iPhone 5, nor anyone anywhere in the world, who is thinking about buying an iPhone 5, will be able to avail of 4G. There is no point really in offering rational consumers a new fountain pen without the ink! As rival competitors continue to enter the game G, the family of competitors grows and new features and functionalities create entropy and adjacent vertices that will limit Apple’s progress unless they join the family.  For example, today in November 2012, Apple is not a key player in social media, digital mobile advertising, OLED Smart-TV, nor is it dominant in cloud computing, NFC and mobile e-wallet payments. They could be in time, many investors hope that they will – sometimes this is not how it works.

Apple can fail: who remembers the Newton in the 1990s? Or the more recent befuddled roll-out its mapping service?  The more we observe G the more convinced we are than it mirrors a game of chess. But is it a game of French defence where it will be challenging for Apple (White) to hold on to the centre as opponent’s attack its Queen (iOS) quickly and swiftly, faster than any counterattack from Apple.  Maybe Apple should stop defending its pawn line of iPod-iPhone-iPad? Acquire a telco. In chess language, Black is out to attack the pawn line. What is Apple’s optimal sequence of moves? Is the ecosystem a sub-game of Alekhine defence by Google (Black) or Android alliance (Black), allowing its King’s Knight (Android) to be positioned across the board so as to weaken White’s centre pawns? We will take up these issues in next Blog entry – our continued recommendation for Apple is to play not to lose rather than play to win.