March 2022

Recency Bias

Recency bias is another common type of cognitive bias in which people’s decisions are influenced by what happened in recent times. An example is the bull and bear runs of the stock market. When the market is having a good time, people assume that it will continue and increase their investments, attracting even more into the bubble. On the other hand, when the market crashes, the trend reverses as more people want to sell, expecting the doom to continue. A lot of analysts, unaware of the bias, carry this fallacy and use the term momentum, a term borrowed from physics, to describe this phenomenon.

Another example is the mass cancellations after aircraft crashes. A recent news report says the cancellation, of close to 9000 flights, following the incident of a China Eastern Airlines flight in March this year. Interestingly this was the first fatal airliner incident in China in the last 12 years!

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Availability Bias

Availability bias is a mental shortcut for decision making that uses what comes to mind based on your impression, i.e. examples that are easily available to you to visualise. The following puzzle from Tversky and Kahneman is a nice one to illustrate this.

Look at the above two pictures and draw structures starting from the top row to the bottom by passing through one and only one X in a row. If you are not entirely sure about the task, let me illustrate it with examples. The following picture gives one such construction on each.

What comes to mind

If your answer is figure 1, then you are not alone. 46 out of 56 participants thought figure 1 has more paths than figure 2. Their median estimate was 40 in Fig 1 and 18 in Fig 2.

A permutation problem

It is a permutation problem that doesn’t need any guessing. Fig 1 calls for 8 ways to draw connections, 3 at a time or a total of 8 x 8 x 8 = 83 = 512 possibilities. The second one? Well, 2 ways, 9 at a time, 29 = 512 (2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2)!

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Microcredit and Grameen Bank

Convincing the bank if you don’t have money or collateral is difficult, if not impossible. It is now easier for the bank to reach its subgame-perfect Nash equilibrium by rejecting the application. Here the bank has done nothing wrong as its primary goal was to protect its business. But in the process, it made the poor out of the credit market, eventually throwing them into a downward spiral. On the other hand, the bank was far more confident with the rich because of the collateral.

Bangladeshi economist Muhammad Yunis, who later got the Nobel Peace Prize for this work, broke this spiral by founding a community development bank, Grameen Bank, employing the microcredit system.

16 Decisions

The banking system works by giving several small loans to a pool of interconnected people. Then, instead of creating any legal framework, the Grameen bank laid a value system by sixteen decisions. Those are aimed to foster discipline, community building, saving, and sustainability.

Introducing Game Theory: Ivan Pastine, Tuvana Pastine
Grameen Bank: Wiki

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Sequential move games and Bank Loans

The interaction between a lender and a borrower is an example of a sequential-move game. The game tree, along with the payoffs, is shown below. A represents the applicant, and B represents the bank.

It is a sequential move game because the applicant gets the chance to invest in the project of her choice only after the bank has released the money.

Based on the payoff, it is easy to find that the bank gets a good deal only when the applicant invests in a safe project. If the bank doubts the applicant’s intention, it will reject the application straight away. In such a case, the applicant has only two choices: 1) convince the bank that she would invest in a safe project, 2) give collateral to guarantee the bank.

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What happened to the Past Climate Predictions?

We have seen the role of climate models to understand the magnitude of global warming. Almost all of the narratives of catastrophe from the climate commentators go back to the output of climate models. And projections from these models play a crucial role in shaping our collective consciousness and aligning global policymaking to fight against this human-made problem.

Models also contribute to why the subject of global warming gets criticism from the sceptics. To most non-physicists, mathematical models represent fantasy, unconnected to reality. Also, projections are forward-looking, and it is easy to cast doubts in public minds for its alleged function as a crystal ball. Calling such people anti-science is easy but not entirely justified; after all, science too calls for the same; get the evidence and validate your predictions. So how do we validate a model prediction for the future?

Look for the past predictions!

Hausfather and others published a paper in the geophysical research letters in 2019 that exactly went for this. The work looked at various models published between the 1970s to the late 2000s. And what did they find? The team have gathered about 15 model predictions from the past and compared them with the observed data. They found that the predictions were well within the margin of errors of the observations. The models of the 70s, 80s and 90s were pretty accurate to predict the future, which is past by now!

What is a climate model?

A model gives a connection between an input and an output. It’s achieved using the physics of the process and represented through the language of mathematics. In the context of climate change, concentrations of CO2 in the atmosphere is the input, and the temperature rise (or fall) is the output. A typical model estimates the reason for the temperature change, i.e., the radiative forcing or the change in energy flux (the incoming – outgoing energy) on the planet. In other words, if the outgoing is less than the incoming, the temperature rises; otherwise, it falls, simple!

Why is this no news?

There are many reasons why a good match between a model and observations never makes it to the news. But, before getting there: why do you expect the predictions made by the collaborative works of 100s of top scientists to go wrong in the first place? We will explore the answer in another post. Now, let’s come back to why they didn’t become headlines. First, predictions happen today (which attracts news), but the data arrive 5-10 years later. By then, you may have forgotten about the original work! Secondly, matching an expectation does not make it sensational for the news. Imagine this news: “NASA scientists verified the physics of radiative forcing, again”! Third, a good match like this is more of a nuisance to the people who want to believe that climate change isn’t real (or who worry about the need to change the current lifestyle).

One such example is the projections made by NASA’s Hansen et al. in 1988. That story, in another post.

References

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Battle of Sexes Continued

We have seen how coordination failure has led the game to a simultaneous move. Now, think about another scenario where there was no network failure, and the communication was possible between A and B. This can lead to another type of game; the sequential move. But before we move on to that, let us look at the original payoff matrix.

B
FootballDance
AFootballA:10, B:5A:0, B:0
DanceA:0, B:0A:5, B:10

In this case, B finishes her job earlier, reaches the dance venue and calls up A. So B becomes the first mover, and A’s strategy now depends on the following game tree (full version).

Now that B has made her move, i.e. dance, the subgame has only the A’s part of the tree.

And the loving A has only one option to select and maximise the couple’s happiness! It has become a subgame perfect Nash equilibrium, favouring the early mover, B in this case.

Not a guaranteed success

Although the present story tells otherwise, there are no rules to guarantee maximum payoff for the first mover. There are several examples where followers benefitted from early movers’ mistakes, especially in businesses that require heavy R&D and are high in fast-evolving technology content. As per this HBR article, gradually evolving technologies and market gives the early mover better chances.

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Battle of Sexes

Battle of sexes is an example of a game with multiple Nash equilibria. So what is it?

A and B are a couple who want to spend the evening together. A likes to watch football, but B prefers dancing. They go to work agreeing to call each other in the evening to meet up. Because of some network issues, they can’t communicate in the evening. So what is the strategy for the couple? Note that it has become a simultaneous move game. Let’s check the payoffs from each other’s point of view.

B
FootballDance
AFootballA:10, B:5A:0, B:0
DanceA:0, B:0A:5, B:10

A knows B has a chance to go to her favourite dance. Therefore, A decides to go to the dance. Since A has no liking for the show, he can’t get the highest payoff, 10, but is still happy to be with B. B, on the other hand, enjoys dancing with her partner.

From B’s angle, A could go for the football he loves. If both end up on the grounds, the payoff will be similar to the previous case, but the roles will be reversed.

Suddenly, the game has two Nash equilibria; a football equilibrium and a dancing equilibrium. So what could really happen? One possibility is a complete lack of coordination, and the Gift of the Magi, the perfect tale of love and sacrifice, re-enacts zero payoff but maximum drama!

Reaching equilibrium

An equilibrium can happen under any of the three circumstances
1) Equal-partner case: they end up at the same place by luck
2) A-dominating case: B has no doubt that A would be at the football place
3) B -dominating case: A knows B is determined to be at her favourite dance floor

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When the Dominant Strategy Leads to Doom

We have seen in the previous post that from a country’s standpoint, it is more advantageous to do nothing for the climate. And let others work for the betterment of you! We’ve also seen that others too, playing their little games, will follow suit, each finding their equilibrium, to the detriment of the whole planet. In other words, individual rationality leads to collective irrationality.

The Paris Climate Accord

The role of the Paris accord is to force countries and bring them to the non-dominant strategy {contribute, contribute}. It can do in the following ways.

First, the Paris agreement is legally binding. So all the signees have to contribute. But here is the catch: the amount of contribution is determined by the individual country through what is known as Nationally Determined Contributions (NDC).

The second option is to provide incentives. Paris agreement provides the framework for financial, technical and capacity building to those who need it. Financial support is necessary to get the capacity building, which, in turn, will reduce the cost through a feature known as the learning rate.

The third option is to impose a cost to non-compliance. As part of the Enhanced Transparency Framework (ETF), countries are required to report back in 2024 and show the actions taken. The process can induce the moral cost to the participating countries, inducing the required push to follow up on promises with actions. Moreover, the measurement, reporting and verification are legally binding.

Paris Agreement: UNFCC

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The Game Called Climate

International cooperation for the climate is an example of game theory with a Nash equilibrium and a dominant strategy. Let’s look at the problem from a country’s viewpoint and construct the payoff matrix. We call it the country MY.

The premise is that the climate crisis is real, but the solution is costly because it requires developing new technologies. If neither the country MY nor the rest makes no attempt to invest, the game ends in total calamity: {(MY:-10), (RE:-10)}. On the other hand, if country MY remains a passive free-rider and the rest of the world does the job, the former get the maximum benefit (MY:12). On the other hand, if country MY makes all the effort, the payoff will be (MY:-15) in great losses for them. Finally, if everybody cooperates according to their respective capacities, all of them will benefit {(MY:10),(RE:10)}. The payoff matrix is

Country MY
Country MY
doesn’t contribute		Country MY
contributes
The RestThe rest
doesn’t contribute
MY: -10, RE: -10MY: -15, RE: 12
The rest
contributes		MY: 12, RE: 8MY: 10, RE: 10

Country MY calculates that it is better placed by not acting, irrespective of what the rest does. They also anticipate that, in such a scenario, the rest will lose more by not working. From an individual country standpoint, this logic of not participating makes it economically advantageous.

But there is an error in this thinking. Any (or all) of the countries in the rest can also follow the suit of Country MY. It leads to a total failure, and no one benefits {-10, -10}

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The Tragedy of Pareto Inefficient Nash Equilibrium

We have seen the prisoner’s dilemma in an older post. The rational decision-maker, the prisoner, will confess because it gives the best outcome, no regret, irrespective of what the other would do. Therefore, it is a Nash equilibrium, named after the American mathematician John Nash – the best response for the prisoner to the choice of the other.

But we know that it, {confess, confess}, is not the best result for either of the players. In other words, the outcome (Nash equilibrium) is not Pareto efficient! A Pareto efficient outcome happens when there isn’t a possible result where someone is better off and nobody is worse off. For this game, Pareto efficiency would have occurred had the prisoners cooperated. But then, confess is the dominant strategy.

Another example of a Pareto inefficient Nash equilibrium is when participants over-consume common resources in what is known as the tragedy of the commons. It is a tragedy as parties out of self-interest consume and deplete the shared resources.

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