The Back of the Napkin

Rule of the game (example tennis)

When we watch a sporting event like a tennis tournament we might hope for a favorite player to win and even feel upset if he loses. However, we don’t often question the rules of the tournament. Lewis Carroll, better known as the author of Alice in Wonderland, explains why the typical tournament structure often fails to award best players the top prizes and offers an alternative method.

In an elimination tournament, each player can only advance along a certain path toward the final. As each player moves through this space, the field is narrowed, until the top prizes are determined. The structure of the space critically influences who finishes well in the tournament. A competition that seems at first glance to be fairly structured to filter out the weaker players may, in fact, not be good at all at selecting the best competitors. In any competition it is not just skill and lucky breaks that determine the winners; the rules of the competition itself determine who will finish well. Many competitions are structured to correctly determine only first place; the second and third prizes are very much subject to chance.

Let us take, as an example of the present method, a Tournament of 32 competitors with 4 prizes.

On the 1st day, these contend in 16 pairs: on the 2nd day, the 16 Winners contend in 8 pairs, the Losers being excluded from further competition: on the 3rd day, the 8 Winners contend in 4 pairs: on the 4th day, the 4 Winners (who are now known to be the 4 Prize-Men) contend in 2 pairs; and on the 5th day, the 2 Winners contend together to decide which is to take the 1st prize and which the 2nd -- the two Losers having no further contest, as the 3rd and 4th prizes are of equal value.

Now, if we divide the list of competitors, arranged in the order in which they are paired, into 4 sections, we may see that all that this method really does is to ascertain who is best in each section, then who is best in each half of the list, and then who is best of all. The best of all (and this is the only equitable result arrived at) wins the 1st prize: the best in the other half of the list wins the 2nd: and the best men in the two sections not yet represented by a champion win the other two prizes. If the Players had chanced to be paired in the order of merit, the 17th best Player would necessarily carry off the 2nd prize, and the 9th and 25th best the 3rd and 4th! This of course is an extreme case: but anything within these limits is possible: e.g. any competitor, from the 3rd best to the 17th best, may, by the mere accidental arrangement of pairs, and by no means as a result of his own skill, carry off the 2nd prize. As a mathematical fact, the chance that the 2nd best Player will get the prize he deserves is only 16/31sts; while the chance that the best 4 shall get their proper prizes is so small, that the odds are 12 to 1 against its happening!

Therefore don't assume that the rules of the game favor the best. The rules of the games are oftentimes predetermined and one can either influence those or even change the entry point into the competition.

Source: BCG, Strategy institute

Clips from Negotiate to Win

• The wise negotiator frequently chooses not to negotiate.
• "It's my bottom line" is the biggest lie in negotiations.
• Only when the other side doesn't move any more can you be sure they're truly at their bottom line.
• Never say you're at your bottom line unless you are.
• Nobody likes having their first offer accepted.
• Schmoozing is the last refuge of the weak negotiator.
• It's better to bring things up now, when you've got some leverage, than later when you don't.
• Never shave a concession. Either make the whole concession that you've supposed to make, or don't make any concession at all.
• The krunch is the simplest and most frequently used tool in negotiating.
• A krunch is the only way to respond to an unreasonable offer.
• Every concession has a price, but krunches cost nothing.
• Only the final handshake seals the deal. Until then, all issues remain open.
• Never stick with an issue that's not working. Skip it and move on to something else.
• The nibble is negotiating's equivalent of a layup.
• Always persuade first. Negotiate only when persuasion fails.
• Face is humankind's third rail. Touch it and die.
• Win-win negotiating is mandatory because the other side survives the talks.
• Don't make a concession without seeking something in exchange.
• Try to avoid saying "no" to the other side. "Yes, if..." is better.
• If you ask for more (without reason) you'll get more.
• Your opening offer should be assertive but never ridiculous.
• Nibbling is part of doing a complete job as a negotiator.
• Sometimes people find satisfactions in strange places.
• Creativity is the most fickle and capricious tool in negotiating.
• The value of the concession to the other side is what matters.
• Setting your Envelopes is your most important homework task.
• Separate the people from the problem. Be hard on the problem but soft on the people.
• We make more concessions to friends.
• The quicker the deal, the greater the risk.
• The more authority you have, the more concessions you'll have.
• Always negotiate with the highest authority person you can get access to.
• Bosses give away the ranch.
• It's where you open, not when, that matters.
• Teams are inherently dangerous, and the bigger the team, the greater the risk.
• Being outnumbered means you're in a target-rich environment.

Decision rules in Ms Pac Man

From a research project in Artificial intelligence where the researchers trained computers to succeed in playing Ms Pac-Man:

When the agent has to make a decision, she checks her rule list, starting with the rules with highest priority. In Ms. Pac-Man, ghost avoidance has the highest priority because ghosts will eat her. The next rule say that if there is an edible ghost on the board, then the agent should chase it, because eating ghosts results in the highest points.

One rule that the researchers found to be surprisingly effective was the rule that the agent should not turn back, if all directions are equally good. This rule prevents Ms. Pac-Man from traveling over paths where the dots have already been eaten, resulting in no points.

What are your heuristics? When are the rules of the game changing and are you changing your actions?

What is strategy

If you can touch it it's tactics, if you can't it's strategy.

Quote: Tiha von Ghyczy

Ants & Algorithms

My friend Martin told me about the Ant algorithm that is used to optimize connections on micro chips. It's a fun approach to solve complex issues like the traveling salesmen riddle:

In the real world, ants (initially) wander randomly, and upon finding food return to their colony while laying down pheromone trails. If other ants find such a path, they are likely not to keep travelling at random, but to instead follow the trail, returning and reinforcing it if they eventually find food (see Ant communication and behavior).

Over time, however, the pheromone trail starts to evaporate, thus reducing its attractive strength. The more time it takes for an ant to travel down the path and back again, the more time the pheromones have to evaporate. A short path, by comparison, gets marched over faster, and thus the pheromone density remains high as it is laid on the path as fast as it can evaporate. Pheromone evaporation has also the advantage of avoiding the convergence to a locally optimal solution. If there were no evaporation at all, the paths chosen by the first ants would tend to be excessively attractive to the following ones. In that case, the exploration of the solution space would be constrained.

Thus, when one ant finds a good (short, in other words) path from the colony to a food source, other ants are more likely to follow that path, and positive feedback eventually leaves all the ants following a single path. The idea of the ant colony algorithm is to mimic this behavior with "simulated ants" walking around the graph representing the problem to solve.

Ant colony optimization algorithms have been used to produce near-optimal solutions to the travelling salesman problem. They have an advantage over simulated annealing and genetic algorithm approaches when the graph may change dynamically; the ant colony algorithm can be run continuously and adapt to changes in real time. This is of interest in network routing and urban transportation systems.

Source: Wikipedia

Running and strategy

Installments in negotiations (Source HBR)

There are other reasons to make concessions in installments. First, most negotiators expect that they will trade offers back and forth several times, with each side making multiple concessions before the deal is done. If you give away everything in your first offer, the other party may think that you're holding back even though you've been as generous as you can be. The manufacturer who offered a 3 percent wage increase to the employees' union up front faced exactly this problem.

Installments may also lead you to discover that you don't have to make as large a concession as you thought. When you give away a little at a time, you might get everything you want in return before using up your entire concession-making capacity. Whatever is left over is yours to keep—or to use to induce further reciprocity. In the real estate example, you might discover that the initial $30,000 increase in your offer was all that you needed to sign the deal!

Finally, making multiple, small concessions tells the other party that you are flexible and willing to listen to his needs. Each time you make a concession, you have the opportunity to label it and extract goodwill in return.

All of the above strategies are aimed at guaranteeing that the concessions you make are not ignored or exploited. It is important to note, however, that when someone refuses to reciprocate, the refusal often hurts her as much as the party who made the concession. Nonreciprocity sours the relationship, making it difficult for negotiators to trust each other or risk further concessions. Thus, effective negotiators ensure not only that their own concessions are reciprocated but also that they acknowledge and reciprocate the concessions of others.