Game Theory, La Tosca and Giacomo Puccini

“I see in this Tosca the opera I need, with no overblown proportions, no elaborate spectacle, nor will it call for the usual excessive amount of music.”

-Giacomo Puccini

Giacomo Puccini was one of the greatest Italian composers, whose operas are played all over the world. His famous works include La Bohème (1896), Tosca (1900) and Madama Butterfly (1904).

La Tosca was drama written by French dramatist Victorien Sardou. Puccini happened to see this drama and was very impressed. He obtained permission from Sardou to convert play into opera.

The drama has three main characters- famous opera singer Floria Tosca, her lover Mario Cavaradossi who is an artist and Baron Scarpia, who heads Rome’s police force.

tosca 1

Floria Tosca is an orphan who is good in singing, and later becomes a famous opera singer. She falls in love with Mario. Mario has a friend Cesare Angelotti, who is a revolutionary and is wanted by Rome’s, police chief Scarpia. Mario helps Angelotti in finding place to hide.

Floria is duped by Scarpia to disclose Angelotti hideout. Angelotti commits suicide to avoid being arrested by police. Mario is arrested and his punishment is execution by firing squad. Floria meets Scarpia, who agrees to spare Mario if she spends one night with him. He will ensure that the firing squad’s rifles will not have real bullets. To save Mario’s life she agrees.


That night Floria meets Scarpia and when he comes near her she stabs him to death. Then she goes to attend mock execution and plans to run away with Mario. But firing squad uses real bullets as Scarpia had no intentions of honouring his commitment and had earlier ordered his team to execute Mario so that he could have Floria for himself.

tosca 2

When Floria sees dead body of Mario, she is unable to bear grief and betrayal and commits suicide by jumping from castle’s parapet.

“As to the play itself, I will only add that it is offensive in its morals, corrupt in its teaching, and revolting in its brutality, and yet everyone who admires acting is bound to see it.”

-Critic on La Tosca

While opera fans world over consider La Tosca as one of the masterpieces of Puccini, the game theorist also fell in love with plot and use it to explain game theory.

The game has two players Floria and Scarpia. The payoff matrix is given below (both in normal and extensive form)

New Microsoft PowerPoint Presentation

Floria has two options, either agrees to Scarpia’s indecent proposal and save life of Mario or reject proposal and watch her lover die.

While Scarpia has two options either agree and have Floria for one night but let her lover live or kill her lover and then try to get Floria.

If both had cooperated Mario would have been alive and Scarpia would have had Floria for one night, payoff was positive for both. But if one of them defects then payoff for that person is much higher ex. Floria will get rid of Scarpia and run away with Mario or Scarpia will have Floria and kill her lover.

Unfortunately, both defect and in such case the payoff is negative for both- defection resulted in death of all three.





Game Theory, Reinhard Selten and Trembling Hand Equilibrium

“I attended workshop on Game Theory at Jerusalem in 1965, It had only 17 participants, but among them all the important researchers in game theory, with few exceptions. Game theory was still a small field. We had heated discussions about Harsanyi’s new theory of games with incomplete information. This was the beginning of my long cooperation with John C. Harsanyi.”

-Reinhard Selten

Reinhard Justus Reginald Selten is a German economist, who won the 1994 Nobel Memorial Prize in Economic Sciences, which he shared with John Harsanyi and John Nash.

Selten further refined Nash equilibrium and came with concept of trembling hand. Game theory assumes that players are rational and not capable of making mistakes.

Selten felt that there exists a small probability of other person making a mistake through what he called “slip of hand” or tremble, wherein a person may choose wrong strategy by mistake.

“My first contact with game theory was a popular article in Fortune Magazine which I read in my last high school year. I was immediately attracted to the subject matter and when I studied mathematics I found the fundamental book by von Neumann and Morgenstern in the library and studied it.”

-Reinhard Selten

Suppose there are two individuals working on a project, a member should take into consideration a possibility of other member unintentionally making an error (a “tremble”).By acknowledging such possibility that other member may take wrong decision, the member chooses a trembling hand perfect equilibrium that takes into account this probability and protects the member should the other member make a mistake.

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There are two students (player A and player B) who wish to join engineering college; they have option of joining civil or mechanical engineering. If you look at payoff matrix, it has two Nash equilibriums.


Player B feels that player A may tremble i.e. there exists a possibility that player A may end up opting for civil engineering while filling form (can happen due to oversight). Suppose probability of oversight is 5%. Suppose player A trembles and opts for civil engineering.

Then expected value for player B is 5% of 4 + 95% of 5= 4.95, so player B will opt only for mechanical engineering ensuring payoff of 5 for himself and in process player A will also benefit.




Hugo Münsterberg, William Marston and Forensic Psychology

“Realize what you really want. It stops you from chasing butterflies and puts you to work digging gold.”

-William Moulton Marston

The word forensic is defined as “the scientific method for investigation of crime”. Forensic psychology is merger of law and psychology.

One of the earliest forensic psychologists was Hugo Münsterberg. Hugo did lot of study on reliability of testimony of eye witness. He wrote about this in his book “On the Witness Stand”.


Münsterberg found out reasons for unreliability in testimony of eye witness. In his book talks about how eye witness testimony is inherently susceptible to what he calls as “illusions” i.e. a subject’s perceptions could be effected by the circumstances, making his/her memory of the events that transpired or testimony inaccurate. He states that with regularity the testimony between two different individuals in the same circumstances can be radically different, even when neither of whom had the slightest interest in changing the facts as remembered.


Münsterberg believed that memory is easily fallible, because one’s memory is affected by the associations, judgments, and suggestions that penetrate into every one of one’s observations and taint out memory and our recollection of events ex. a person may read some facts about case in newspapers which he may not be knowing and this may influence his memory.


“The lawyer alone is obdurate. The lawyer and the judge and the juryman are sure that they do not need the experimental psychologist . . . They go on thinking that their legal instinct and their common sense supplies them with all that is needed and somewhat more . . . Just in the line of the law it therefore seems necessary not to rely simply on the technical statements of scholarly treatises, but to carry the discussion in the most popular form possible before the wider tribunal of the general reader”

-Hugo Münsterberg

During his lectures at Harvard University, he used to conduct an experiment. He used to show his students a large sheet of white cardboard with a certain number of black dots on it spread in an irregular order. He exposed it for the students to view for only five seconds, and then asked them how many black dots that they thought were on the sheet. Hugo description of results is given below.

“The results were surprising in that even with “highly trained, careful observers, whose attention was concentrated on the material, and who had full time for quiet scrutiny… there were some who believed that they saw seven or eight times more points than some other saw.”

One of his students was William Marston. Marston was law graduate, who was doing doctorate in Psychology from Harvard University. Marston was a talented student. With the help of his wife Elizabeth he developed the systolic blood pressure test of deception. The rationale behind the test was simple enough: when people lied, their elevated autonomic arousal could be measured through systolic blood pressure (later expanded to include galvanic skin response). He claimed that this method had 97-99% accuracy rate.


In US a person called James Frye killed another person called Brown. Frye was later arrested and given death penalty. Frye claimed that he had not killed Brown. Lawyers of Frye decided to invite Marston and asked him to use his deception test instrument to find out if Frye was telling truth.

Marston conducted deception test in jail and came to conclusion that Frye was telling truth.

"It was my upbringing, I was smacked on my bottom when I was born."

Unfortunately Judge McCoy had no faith his Marston’s instrument and its results. He declared that deception test was unreliable and Frye was guilty of murder.

“I gave him a deception test in the District jail. No one could have been more surprised than myself to find that Frye’s final story of innocence was entirely truthful! His confession to the Brown murder was a lie from start to finish”

-William Marston on James Frye


William Marston later wrote book called “Emotions of Normal People”. This book resulted in DISC psychometric test. Marston did not claim any copyrights over his idea. DISC today is available under various brands like DiSC, Extended DISC, Thomas Profiling etc.


Marston came up with idea of a superwoman who fights for truth, which took shape of Wonder Woman series.


Game Theory, Principal-Agent Problem & Arthur Andersen

“As the firm grew from a close-knit partnership to a globe-spanning behemoth, pressure to boost profits became intense. Andersen leaders responded by pushing partners to become salesmen — upsetting the delicate balancing act any auditor must perform between pleasing a client and looking out for the public investor.”

-Ken Brown, The Wall Street Journal

In game theory there is interesting concept of Principal- Agent Problem, which is also called as Agency Theory.

It belongs to the category of games with imperfect information in which one player (the principal) attempts to offer incentives to the other (the agent) to encourage the agent to act in the principal’s best interest.

An agency is the relationship between two parties, where one is a principal and the other is an agent who represents the principal in transactions with a third party. Agency relationships occur when the principals hire the agent to perform a service on the principals’ behalf. Principals commonly delegate decision-making authority to the agent’s ex. relationship between shareholders (Principals) and Managers (Agents).



The problem arises where the two parties have different interests and asymmetric information (the agent having more information); such that the principal cannot directly ensure that the agent is always acting in its (the principal’s) best interests.


The principal-agent problem also develops when a principal creates an environment in which an agent has incentives to align its interests with those of the principal, typically through incentives.

“Waste Management paid Andersen $17.8 million in fees unrelated to the audit between 1991 and 1997, against audit fees of $7.5 million.”

-The Wall Street Journal




A good example of this is relationship between auditing firm Arthur Andersen (agent) and its clients like Enron, Waste Management, and WorldCom (principal). The principal had hired agent for auditing their books. But soon Andersen also started given non audit services to the clients ex. consulting services. The principal designed incentive structure in such a way that agent was more interested in non audit related services than doing their actual job. This created conflict of interest and soon Andersen was helping clients in committing financial frauds.


“The quiet dilution of standards and the rise of auditor-salesmen at Andersen are central to the scandals that have cost investors billions of dollars, eliminated thousands of jobs and threatened the retirement security of millions of citizens.”

-Chicago Tribune

Combinatorial Games, Zugzwang and Employee Exit

Chess is timing, so is Life!        

Move with a purpose, Have high aims!

Hold on! Take charge and command.

Do the best and leave the rest to God!

And he will save your position from the critical Zugzwang!

-Niranjan Navalgund

Combinatorial games are two-person games with perfect information and no chance moves, and with a win-or-lose outcome. Such a game is determined by a set of positions, including an initial position, and the player whose turn it is to move. Play moves from one position to another, with the players usually alternating moves, until a terminal position is reached. A terminal position is one from which no moves are possible. Then one of the players is declared the winner and the other the loser. Examples of such games are Chess, Checkers etc.


In combinatorial game there is an interesting term called as Zugzwang. Zugzwang is a German word meaning “obligation to move”. The term is used for a position in which whoever has the move would obtain a worse result than if it were the opponent’s turn to play. A player is said to be “in zugzwang” when any possible move will worsen his position.




In corporate life, when an employee is asked to resign, he is given two options either he resigns on his own or his services are terminated. Any move results in loss to employee as he is in zugawang.

'Would you prefer a quick termination or a slow, painful phaseout?'