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18 Oct

Strategy Essentials: Game Theory — Part 3

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In the last piece in this series, we looked at how reward structures and individual incentives of a game create scope for dominant strategies to play out.

(Link to Part 1 and Part 2)

To refresh your understanding before we begin:

A Dominant Strategy Solution is quite straightforward. In a game, if there exists a strategy for a player that yields the highest payoff regardless of what the other players choose, this strategy is deemed dominant.

You, as a player, would choose this strategy every time, because no matter what tomfoolery the others are up to, this strategy ensures you the highest payoff. It's the equivalent of having a royal flush in a game of poker or having the legal system or the top politician in your pocket; it trumps all other hands or strategies, no matter what.

On the other hand, a Nash Equilibrium is more nuanced. It emerges from a scenario where each player’s strategy is optimal given the strategies chosen by the others.

In this equilibrium, no player has an incentive to deviate from their chosen strategy after considering an opponent's choice. Everyone’s holding their breath, making the best move they can, given the moves of the others.

Unlike a Dominant Strategy Solution, a Nash Equilibrium doesn’t require a strategy to be superior in all scenarios, but rather it emanates from a mutual best response.

But strategy is not that straightforward. There are some more nuances.

To predict what type of game or strategy plays out, the context or the environment in which a game occurs is also crucial.

For instance, the type of strategy a player will use in a chess game will be completely at odds with what type of strategy someone playing rock-paper-scissors will use.

It would be foolish if you tried to be extremely methodical while playing rock-paper-scissors or equally random while playing chess. The context surrounding both games, the rules of the gameplay, and how winners are decided are totally different in both games.

So, if you zoom out, and look at different kinds of gameplay, typically, three types of gameplay emerge:

1. Sequential games
2. Simultaneous games
3. Dynamic games [a mix of sequential and simultaneous games]

Let’s take a look at these gameplays and understand why predicting a way to win or predicting the next move or a dominant strategy isn’t as simple as it may seem.

Sequential Games

Imagine a game of chess. It’s a classic turn-by-turn battle of wits. You make a move, then I make mine, and we keep going until one of us wins or we end up in a stalemate.

But is there a dominant strategy, a surefire way to win every time? Not really.

Even with well-crafted opening moves, victory isn't guaranteed. Each game unfolds uniquely, and a large part of the fun is adapting to the ever-changing scenarios on the board. The order of moves and the anticipation of the opponent's responses is a fundamental aspect of the game.

Similarly, consider a project management scenario where a team is tasked with completing a project with multiple stages.

Each team member has to make decisions sequentially, such as selecting which task to work on next. The order in which team members make their decisions can impact the project's progress and efficiency. If one team member delays their task, it may affect the timeline for others, creating a sequence of interdependent decisions.

A game theorist calls these games sequential because they follow a series of action-reaction loops between the players.

These games often require players to think not only about their immediate actions but also about how their choices influence subsequent moves, making strategic thinking a key component.

But just because the game is sequential, the likelihood of a dominant strategy emerging isn’t a guarantee.

In chess, each player takes turns making moves, and the sequence of moves is essential for the game's outcome. And while there are well-established opening strategies in chess, there is no single overarching dominant strategy that guarantees victory. There might be strictly dominant plays in the course of the game, sure, where you or your opponent may strictly be at an advantage. But there's no single dominant strategy for the whole game.

Hence, what works as a strong move in one situation may not be as effective in another due to the evolving nature of the play.

Whereas in tic-tac-toe, a dominant strategy emerges in the sequential game. Player one, whose incentive is to score three Xs or Os in a row, can force a win by making the first move smartly.

Simultaneous Games

Now, think of Rock-Paper-Scissors. We both make our moves at the same time, without a clue about what the other is choosing.

It’s a guessing game, and there’s no dominant strategy to secure a win. Unlike chess, there’s no reacting to the previous move because everything happens in a flash. And that uncertainty is what makes these games so unpredictable and exciting.

Alternatively, think of a scenario where multiple bidders participate in an auction, such as an online auction for artwork. Bidders submit their bids simultaneously without knowing the amounts other bidders are willing to pay.

The highest bidder wins the item and pays their bid amount. This situation represents a simultaneous game where each bidder selects their bidding strategy independently.

Unlike sequential games, where players learn about the moves made by their opponents, in simultaneous games, players must anticipate their opponents' choices while selecting their own strategies.

This, in turn, makes it difficult for dominant strategies to play out, if you cannot map out all scenarios like you can in a simple scenario like the Prisoner's Dilemma.

The Prisoner's Dilemma is a simultaneous game where confessing is a dominant strategy and also leads to a Nash Equilibrium. So it's possible to identify dominant strategies even in simultaneous games, if they exist, provided you can map out the entire universe of decisions and payoffs within the game.

But more complex and multifaceted simultaneous games breed uncertainty, which is the mainstay of most gameplay in the real world.

Dynamic Games

These games combine elements of both sequential and simultaneous actions. Players might react to others' actions, but there could also be simultaneous moves happening at different stages of the game.

Consider a political campaign. Parties react to each other’s policies (sequential), but they also make strategic decisions like funding allocation simultaneously without knowing the others’ exact plans.

Or say, a soccer match. Teams react to goals scored and adjust strategies (sequential), but within the game, players are often making moves concurrently, unaware of the precise moves opposing players will make at that moment.

But say you're in the FIFA World Cup playoffs and you know that you're in extra-time and lagging behind your competition by one goal. Losing would mean getting kicked out of the World Cup. Scoring that goal would mean going to extra time or penalties and having the opportunity to score over your opponents.

So, what do you do?

You make your goalkeeper a part of the scoring team and invite him in the six-yard area to receive a corner kick. The worst downside to that is the opposition scoring one more goal in the counter-attack. But you were already going to lose, so it doesn't make the downside any worse for you. The upside, however, is potentially going on to lift the World Cup.

So, the strictly dominant strategy in this situation is to make your goalkeeper a part of the striking unit, and that is what you see every team do in this situation.

I hope you can see how contextual dominant strategies can be, according to the game and the stage of the gameplay.

And because most of the business world, your professional and personal life is a sequence of simultaneous games, devising an overarching dominant strategy may be a futile pursuit in the long run.

But that isn't to say that dominant plays do not exist.

Dominant strategies are more likely to emerge when one player can exert a substantial influence on the game's dynamics and has a clear advantage over others.

Companies with substantial market share often have the leverage to dictate terms. For instance, consider Apple with its pricing strategy. Their strong brand, intellectual IP, and design philosophy allow them to price their products at a premium — an advantage not shared by many competitors. Add the cultural signaling value its products offer and Apple becomes unbeatable.

It can price exorbitantly and refuse to change its pricing strategy, simply because it knows it has many competitive advantages that cannot be easily arbitraged away.

Think of even Google or Facebook, for that matter. They can increase their ad revenues without a whisker of worry and marketers will simply have no option but to comply with them.

These companies are playing dominant strategies with unique moats that are hard to compete with.

And sometimes, dominant strategies emerge from regulation or cultural perception, too.

For instance, renewable energy adoption or just buying carbon credits to assuage climate warriors might become a dominant strategy for companies in regions with stringent carbon emission regulations or where the demographic looks down upon businesses that pollute the environment.

There is no upside to not doing it, but there's a steep downside in terms of long-term reputation. So, signaling eco-friendliness just becomes a dominant strategy.

When it comes to careers, a dominant position to be in is to not need a job.

Because that way, you can play a strictly dominant strategy of commanding a high price for your services and being picky about clients or companies you choose to work with. Because the downside to that strategy is not getting a gig — something you would be perfectly fine with.

So you either get paid handsomely or you don't work at all. It's a dominant strategy followed by people who are excellent at their craft and have built a reputation for quality work. Most of us do not fit into that bucket. So we cannot follow straightforward and rigid dominant strategies and have to keep adjusting and adapting to the market.

Moral of the story?

Be attentive to the players in a game: their skills and resources, incentives, and rewards.

Build the ability to map out decisions and payoffs for increasingly complex and multivariate matrices for iterated gameplays.

And don’t rush. Because only fools rush in where angels fear to tread.

(Unless it's the dominant strategy for the game you're playing or the stage of the gameplay you're at currently.)

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